# 4. Describe the behavior of the graph at the x-intercepts for the function f(x) = (2x-7)^7 (x+3)^4. Be sure to identify each x-intercept and justify your answer.  How does each exponent change the look of the graph at the x-axis?

38,702 results
1. ## Algebra

11. What are the x-intercepts of the graph of the quadratic function f(x) = 5x2 + 4x – 1?

2. ## math

the graph of a quadratic function has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine an expression for the function.

3. ## algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

4. ## MATH

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

5. ## math

1. Consider the function f(x) = x3 + 7x2 + 2x - 40 . a. Find the possible rational roots of f(x) = 0. b. Use synthetic division to divide f(x) by x - 2. Show all your work. Use your answer to explain whether or not x – 2 is a factor of f(x). c. Factor

The graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation? Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and

7. ## ALGEBRA 1 HELP

The description below represents Function A and the table represents Function B: Function A The function is 2 more than 5 times x. Function B x y -1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions? Their slopes are

8. ## algebra

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

9. ## Precalc

Find an equation of a rational function that satisfies the given conditions. Vertical asymptote: x = 4 Horizontal asymptote: y = 0 X-intercepts: none Y-intercepts (0, -1/4) Multiplicity of 1 Removable discontinuity: x = 1 End behavior: x --> infinity, f(x)

10. ## Trigonometry

Graph the function y=2sin(x-2pi/3). To draw the graph, plot all x-intercepts, minima and maxima within on period. I need to graph at least 5 points. I have -pi, 0, pi, 2pi, 3pi, and 4pi along the x-axis

11. ## Functions

The function y = x becomes y= -2(3x+2)-5. Describe the order in which the transformations would take place. 1. The function is stretched vertically by a factor of 2 2. The function is compressed horizontally by a factor of 1/3 3. The graph is reflected

12. ## Math

If a graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation? Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and

13. ## Pre-Calculus

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of

14. ## Math

1. Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point. x-intercepts: 2,3 point: (4,2) 2. Write a quadratic function in standard form whose graph passes through the given points.

15. ## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

16. ## Algebra II

Describe the end behavior of the graph of the polynomial function by completing these statements: f(x)→? as x→-∞ and f(x)→? as x→+∞. 1. f(x)=-(x^2)+1 2. f(x)==10x^3

17. ## Algebra Help me Please

Someone please help me with this!!! Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle

18. ## College Algebra

1.Answer the following for the given quadratic function. f(x) = -2x^2 - 8x - 13 (a) does the graph of f open up or down? (b) what is the vertex (h,k) of f? (c) what is the axis of symmetry? (d) what are the intercepts? (e) how is the graph suppose to look

19. ## ALGEBRAA

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

20. ## Calculous

Describe in words the long run behavior as x approaches infinity of the function y = 6x^6 + (4x^4/x^-9) -9x^7+3 I know y goes to positive infinity as x approaches infinity The graph resembles ? (is it 4x^5) I tried simplifying 4x^4/x^-9 and got 4/x^-5 is

21. ## college algebra

Given the following quadratic equation, find a. the vertex b. the axis of symmetry c. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function.

22. ## math pre calculus

find the following for the function f(x)=(x+5)^2(x-2)^2 a.find the x and y intercepts, b.find the power function that the graph ressembles for large values of x c.determine the maximum number of turning points on the graph of f d.determine the behavior of

23. ## Algebra 2

Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function.y=x^4-2x^2-x-1 and y=(x-3)(x+1)(x+2)

24. ## math

Consider the function f(x)= 3 ------. x^2-25 a) Determine any restrictions on x. b) State the domain and range. c) State equation(s) for the asymptote(s). d) Determine any x- and y-intercepts. e) Sketch a graph of the function. f) Describe the behaviour of

25. ## algebra

the graph of a first degree absolute value function has a Y-intercept of 3, x-intercepts of -9 and -3 , and a minimum vlaue of -3 at x=-6. on the axes provided , sketch a graph of this function.

26. ## math

. Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range, (f) intervals where the function is increasing, (g) intervals where the function is decreasing, and (h) the graph of the function.

27. ## Fullerton

Graph each function considering the domain, critical points, symmetry regions, where the function is increasing or decreasing, inflection points where the function is concave up or down, intercepts where possible and asymptote where applicable f(x)= x^4-

28. ## college algebra

Given the following quadratic equation, find;? a. the vertex b. the axis of symmetry c. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function.

29. ## Algebra

analyze the graph f(x)=(x-2)^3(x-3)^2(x-4) a)end behavior: find the power function that the graph of f resembles for large values of absolute value of x

30. ## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

31. ## PHYSICS

What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in Fig. 15-30 if the position function x(t) has the form x = xmcos(ωt + φ)? The vertical axis scale is set by vs = 5.50 cm/s. Since i cant

32. ## Algebra 2

Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function. Number one: y=x^4-2x^2-x-1

33. ## Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any

34. ## Algebra

Please describe the end behavior of the graph of the function below. f(x) = –2x^5 – x^3 + x – 5?

35. ## algebra

1.Graph the function f(x) = (x + 3)3 by hand and describe the end behavior

36. ## trig

Graph three periods of the function. (identify period and phase shift and intercepts) y = f(x) = √3/2 sin(2x) - 1/2 cos(2x) if you can't graph it can you at least get it into that simpler form which is graph able.

37. ## Math

Graph y=5^x and y=log_5 x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function

38. ## Algebra

1. In the formula S=a1(1−r), what restrictions are placed on the variable r? 2. The formula A=12bh can also be expressed as A=bh2. Do you agree? 3. If x and y are real numbers, and xy=0, then either x=0 or y=0. Do you agree? 4. Do the inequalities xlogx?

39. ## Math-due today, need a check

Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.

40. ## precalculus

analyzethe graph of the function Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (c) Find the maximum number of turning points. (d) Graph the function Please show

41. ## College alg

Analyze the graph of the following function as follows: (a) Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (c) Find the maximum number of turning points.

42. ## calculus

I have two questions, please help. 1. Uss completing the square to describe the graph of the following function. Support your answers graphically. f(x)= -2x^2+4x+7 please show work. 2. Can someone help me to graph this function? f(x)=x^2-6x+5 Then find the

43. ## Math

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

44. ## algebra 2

Graph the function f(x) = –3x^3 + 9x^2 – 2x + 3 using graphing technology and describe the end behavior

45. ## Algebra

Please Help Guys! 1) Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? A.The expression has a constant outside of the squared term. B. The expression is not the product of two binomials. C. The variable x has a coefficient. D. Some of the terms

46. ## algebra

list the domain and the x- and y- intercepts of the following function. Graph the funciion. Graph the function. Be sure to label all the asymptotes.

47. ## Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?

48. ## Algebra 2

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

49. ## Math2

Sketch the graph of this quadratic function: f(x)= 3(x-2)^2 -10. Be sure to explain the steps you take. **I don't need help with the graph part but I need to find the x and y intercepts, the equation of the axis of symmetry and the coordinates of the

50. ## math

Which three options are true about the quadratic equation?? y= 4t^2 + 16t + 18 A. The graph has a minimum. B. The graph of y crosses the horizontal axis at t = 10 and t = 20. C. The equation 4t^2 + 16 + 18 = 6 has one real solution. D. The function has a

51. ## algebra

2. The function f is defined as follows f(x)={4+2x if x0 a) Find the domain of the function b) Locate any intercepts c) Graph function d) Based on graph find range e) Is f continuous on its domain? a) The domain of the function f is

52. ## Algebra U4 L25

While performing a vertical line test on a graph, you notice that the graph intercepts the vertical line twice. Which of the following correctly interprets the result of the test? Because the vertical line intercepted the graph more than once, the graph is

53. ## Math

1. determine the interval(s) where the function f(x)= -1 / 2x+10 is a) positive b) Increasing 2. Consider the function f(x) = 3 / 4x-5 a) Determine the key features of the function: i) Domain and range ii)Intercepts iii) Equations of any asymptotes iv)

54. ## Math

4. Describe the behavior of the graph at the x-intercepts for the function f(x) = (2x-7)^7 (x+3)^4. Be sure to identify each x-intercept and justify your answer. How does each exponent change the look of the graph at the x-axis?

55. ## Calculus

Given the function f(x)= x√(x+3), Indicate the domain of f(x): ………………………… What are the x – intercepts of the graph of f(x)? POINTS! ……………………………. Identify the critical points of f(x) (write pairs of coordinates,

56. ## ALGEBRA

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

57. ## MATH TRIGONOMETRY

refer to the polynomial function f(x)= -x(x-1)(x+2) in anwering the folloowing questions. 1.what is the y intercept? 2.what is the behavior of the left end of its graph? 3.will the graph pass through the origin? 4,what is the behavior of the left end of

58. ## College Algebra

Using the 7 steps outlined in section 4.3 of your book, analyze the graph of the following function: R(x) = x^2 - 49/x^4 - 16 Step 1: Factor the numerator and denominator of R and find its domain. If 0 is in the domain, find y-intercept, R(0), and plot it.

59. ## Pre-Calculus

(I NEED URGENT HELP FOR THIS) Given the info. that a rational function has a vertical asymptote of x=3 and x=-3, horizontal asymptote at y=-4, no x-intercepts, and y-intercept: (0,2/3), no removable discontinuity, and no end behavior, what would the

60. ## Math

Describe the end behavior and estimate the x-and y-intercepts for each function. Estimate to the nearest tenth when necessary. y=-2x^5+x^3

61. ## Alg

describe the end behavior of the graph of the polynomial function. Then evaluate the ntion for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. I'm confused on this. Help.

62. ## math, algebra,graphs help

THe directions state: (A)Complete the table, (B) describe the resulting graphs by identifying the vertex point, (C)the graph’s direction, (D) and any axis intercepts gleaned from the table or graph Problem #3 Equation : y = 2x^2 My answers: A) Table:

63. ## Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?

64. ## mathematics

find the x-intercepts and y-intercepts of the function f(x)=x^2 +6x +9 and the graph function

65. ## limit from graph

How do I know if the limit of a function exists or not from that function's graph. Thanks. It the graph of a function becomes straighter at + and -infinity, it means that the function behaves linearly in the limit. However there may be other types of

66. ## College Algebra

1.The graph of y = - 1/2 |x - 5| - 3 can be obtained from the graph of y = |x| by which transformations? What is the horizontal shift? By what factor is the graph stretched or shrunk vertically and how is it reflected? What is the vertical shift? 2. Find

67. ## algebra

find the following for the function f(x)= (x+5)^2(x-1)^2 a) find the x and y intercepts for the polynomial function f b) determine whether the graph of f crosses or touches the x axis at each x intercept C) put all information together to obtain the graph

68. ## Math

Find the x- and y-intercepts and graph the equation plotting the intercepts. Please show all of your work. Submit your graph to the Dropbox 2x-3y=9

69. ## Algebra 2

These 3 equations all describe the same quadratic function. What are the coordinates of the following points on the graph of the function? From which equation is each point most easily determined? y = (x - 5) (x + 1) y = x^2 - 4x - 5 y = (x - 2) ^2 - 9

70. ## College algebra

Given the following quadratic equation find. a) the vertex b) the axis of symmetry c) the intercepts d) the domain e) the range f) the interval where the function is increasing g) the interval where the function is decreasing h) graph the function y=

Given the following quadratic equation find. a) the vertex b) the axis of symmetry c) the intercepts d) the domain e) the range f) the interval where the function is increasing g) the interval where the function is decreasing h) graph the function y=

72. ## math

Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible. The

73. ## I need help with these please ALGEBRA

1. Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 2. Evaluate : sqrt7x(sqrtx-7sqrt7) show your work. 3. Solve the equation. Check for

74. ## Calculus

Suppose f(x)= e^(-1/x). Graph this function in the window -5(

75. ## Calculus

Suppose f(x)= e^(-1/x). Graph this function in the window -5(

76. ## algebra II

Can you please help me with the these problems. 8.Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 11x^2, but which has its vertex at (2, 9). 10. Use the vertex and intercepts to sketch the graph of the

77. ## calculus II

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity?

78. ## math

Please help me! f(x)=(x+1)^3-2 1. How do I find the x and y intercepts, if any? 2. Describe the long term behavior of this function. Give the power function that F resembles.

79. ## math 11

4. a)how many different x-interceps could the graph of a quadratic function have? explain. it can have more than one because a parabola is a curved line on a graph in which case it touches two or more different points on the x-axis b)how many different

80. ## math

find the x-intercepts for P(x)= x^4-10x^2+9 and determine the behavior of the graph near the intercepts

81. ## Calculus

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity?

82. ## graph of a polynomial

Sketch the graph of 1/12(x+2)^2(x-3)^2 and make sure the graph shows all intercepts and exhibits the proper end behavior. I can sketch the graph but how do I do the second part? Thanks What does the function do at x= inf, or x= -inf. That is the end

83. ## Math

Describe the end behavior and estimate the x-and y-intercepts for each function. Estimate to the nearest tenth when necessary. y+-2x^5+x^3

84. ## MATH

1.Graph the function f(x) = (x + 3)3 by hand and describe the end behavior.

find the slant asymptote of the graphof the rational function. 1.f(x)=x^2-x-2/x-7 y=? 2. determine the symmetry of the graph of f. a. the graph has y-axis symmetry f(-x)=f(x) b. the graph has orgin symmetry f(-x)= -f(x) c. the graph has both y-axs and

Please explain to me how to do the following problems, I don't understand them. Thanks! Find the x-intercepts (if any) for the graph of the quadratic function. 1.f(x) = (x + 2)2 - 4 Find the y-intercept for the graph of the quadratic function. 5.y + 9 = (x

87. ## Help !

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

88. ## Pre-Calculus

1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x-6. 2) Use a graphing utility to graph the function and determine the x-intercepts and B. set y=0

89. ## Pre-Calculus

Radical Functions Graph y=(x-3)(x+2) and y=√(x-3)(x+2). where are the x-intercepts of each function ?why? for the first one, i know that whatever is inside the brackets is opposite, so the x intercepts would be at 3, and -2. but the whole radical thing

90. ## Pre-Calculus

Graphing Polynomials Decide whether each of the following is sometimes true, always true, or never true and explain reasoning. A. A cubic function has 2 different x-intercepts ^Never true, has to have 3? B. A cubic function has 3 x-intercepts ^ Always true

91. ## pre calculus

find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find the x and y intercept of the polynomial function f. b.)find the power function that the graph of f ressembles for large values of lxl. c.)determine the maximum number of turning pointsof the

92. ## Math

Find two quadratic functions whose graph have the given x-intercepts. Find one function whose graph opens upward and another whose graph open downdward. (-5/2,0),(-2,0)

1. a). Calculate (x^5+9x^4-3x^3+5x+8) / (x^2+3x+1) using long division. b). Write a division statement. 2. Calculate (-2x^4 +x^3-8x^2+11) / (x-6) using synthetic division. 3. Determine the domain, intercepts, asymptotes (if any), and positive/negative

94. ## College Algrbra

Given the following quadratic equation, find a. the vertex b. the axis of symmetry. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function

95. ## Algebra,Math, graphs help

This is what the directions state to do: (A) Complete the table,(B)describe the resulting graphs by identifying the vertex point, (c) the graph’s direction, (d) and any axis intercepts gleaned from the table or graph. Problem #1 Equation is : y = -x + 1

96. ## Pre cal

)a function f is defined as f(x) = 3*2^x describe the end behavior of f, please describe in detail how you got the answer and explain your abbreviations.

97. ## algebra2

What are the x-intercepts for the graph of the quadratic function f(x)=1/4(x +2)^2-9

98. ## Intermediate Algebra

Find the x- y-intercepts and graph the function f(x)=5x-10

99. ## Math/Algebra

Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.

100. ## Math

The distance d1 in miles, a small plane is from its final destination is given by d(t) = 250 – 100t, where t is the time, in hours, remaining for the flight. Find and discuss the meaning of the intercepts of the graph of the function. (You must first
### Content Structure
The text passage is a collection of questions and problems related to graphing and analyzing polynomial functions, particularly focusing on quadratic functions. The questions cover various aspects such as finding x-intercepts, y-intercepts, vertex, axis of symmetry, and describing the end behavior of the functions.

### Analysis
multiple_questions

1. **question 1:**
   - **content:** describe the behavior of the graph at the x-intercepts for the function \( f(x) = (2x-7)^7 (x+3)^4 \).
   - **analysis:** this question asks for the behavior of the graph at the x-intercepts, which are \( x = \frac{7}{2} \) and \( x = -3 \). the behavior is determined by the exponents of the factors. at \( x = \frac{7}{2} \), the graph crosses the x-axis because the exponent is odd. at \( x = -3 \), the graph touches the x-axis and turns back because the exponent is even.

2. **question 2:**
   - **content:** what are the x-intercepts of the graph of the quadratic function \( f(x) = 5x^2
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 4. Describe the behavior of the graph at the x-intercepts for the function f(x) = (2x-7)^7 (x+3)^4. Be sure to identify each x-intercept and justify your answer.  How does each exponent change the look of the graph at the x-axis?

38,702 results
1. ## Algebra

11. What are the x-intercepts of the graph of the quadratic function f(x) = 5x2 + 4x – 1?

2. ## math

the graph of a quadratic function has x-intercepts -1 and 3 and a range consisting of all numbers less than or equal to 4. Determine an expression for the function.

3. ## algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

4. ## MATH

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

5. ## math

1. Consider the function f(x) = x3 + 7x2 + 2x - 40 . a. Find the possible rational roots of f(x) = 0. b. Use synthetic division to divide f(x) by x - 2. Show all your work. Use your answer to explain whether or not x – 2 is a factor of f(x). c. Factor

The graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation? Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and

7. ## ALGEBRA 1 HELP

The description below represents Function A and the table represents Function B: Function A The function is 2 more than 5 times x. Function B x y -1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions? Their slopes are

8. ## algebra

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

9. ## Precalc

Find an equation of a rational function that satisfies the given conditions. Vertical asymptote: x = 4 Horizontal asymptote: y = 0 X-intercepts: none Y-intercepts (0, -1/4) Multiplicity of 1 Removable discontinuity: x = 1 End behavior: x --> infinity, f(x)

10. ## Trigonometry

Graph the function y=2sin(x-2pi/3). To draw the graph, plot all x-intercepts, minima and maxima within on period. I need to graph at least 5 points. I have -pi, 0, pi, 2pi, 3pi, and 4pi along the x-axis

11. ## Functions

The function y = x becomes y= -2(3x+2)-5. Describe the order in which the transformations would take place. 1. The function is stretched vertically by a factor of 2 2. The function is compressed horizontally by a factor of 1/3 3. The graph is reflected

12. ## Math

If a graph of a quadratic function can have 0, 1 or 2 x-intercepts. How can you predict the number of x-intercepts without drawing the graph or (completely) solving the related equation? Suppose that the graph of f(x) = ax^2+bx+c has x-intercepts (m,0) and

13. ## Pre-Calculus

For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the intervals over which the graph of

14. ## Math

1. Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point. x-intercepts: 2,3 point: (4,2) 2. Write a quadratic function in standard form whose graph passes through the given points.

15. ## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

16. ## Algebra II

Describe the end behavior of the graph of the polynomial function by completing these statements: f(x)→? as x→-∞ and f(x)→? as x→+∞. 1. f(x)=-(x^2)+1 2. f(x)==10x^3

17. ## Algebra Help me Please

Someone please help me with this!!! Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle

18. ## College Algebra

1.Answer the following for the given quadratic function. f(x) = -2x^2 - 8x - 13 (a) does the graph of f open up or down? (b) what is the vertex (h,k) of f? (c) what is the axis of symmetry? (d) what are the intercepts? (e) how is the graph suppose to look

19. ## ALGEBRAA

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

20. ## Calculous

Describe in words the long run behavior as x approaches infinity of the function y = 6x^6 + (4x^4/x^-9) -9x^7+3 I know y goes to positive infinity as x approaches infinity The graph resembles ? (is it 4x^5) I tried simplifying 4x^4/x^-9 and got 4/x^-5 is

21. ## college algebra

Given the following quadratic equation, find a. the vertex b. the axis of symmetry c. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function.

22. ## math pre calculus

find the following for the function f(x)=(x+5)^2(x-2)^2 a.find the x and y intercepts, b.find the power function that the graph ressembles for large values of x c.determine the maximum number of turning points on the graph of f d.determine the behavior of

23. ## Algebra 2

Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function.y=x^4-2x^2-x-1 and y=(x-3)(x+1)(x+2)

24. ## math

Consider the function f(x)= 3 ------. x^2-25 a) Determine any restrictions on x. b) State the domain and range. c) State equation(s) for the asymptote(s). d) Determine any x- and y-intercepts. e) Sketch a graph of the function. f) Describe the behaviour of

25. ## algebra

the graph of a first degree absolute value function has a Y-intercept of 3, x-intercepts of -9 and -3 , and a minimum vlaue of -3 at x=-6. on the axes provided , sketch a graph of this function.

26. ## math

. Given the following function, f(x)=-x^2 -8x find: (a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e) range, (f) intervals where the function is increasing, (g) intervals where the function is decreasing, and (h) the graph of the function.

27. ## Fullerton

Graph each function considering the domain, critical points, symmetry regions, where the function is increasing or decreasing, inflection points where the function is concave up or down, intercepts where possible and asymptote where applicable f(x)= x^4-

28. ## college algebra

Given the following quadratic equation, find;? a. the vertex b. the axis of symmetry c. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function.

29. ## Algebra

analyze the graph f(x)=(x-2)^3(x-3)^2(x-4) a)end behavior: find the power function that the graph of f resembles for large values of absolute value of x

30. ## pre - CALCULUS

Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to describe the graph the given function. h(x) = 2 | x | + 2

31. ## PHYSICS

What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in Fig. 15-30 if the position function x(t) has the form x = xmcos(ωt + φ)? The vertical axis scale is set by vs = 5.50 cm/s. Since i cant

32. ## Algebra 2

Describe the end behavior of the graph of the polynomial function. Then evaluate the function for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. Then graph the function. Number one: y=x^4-2x^2-x-1

33. ## Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any

34. ## Algebra

Please describe the end behavior of the graph of the function below. f(x) = –2x^5 – x^3 + x – 5?

35. ## algebra

1.Graph the function f(x) = (x + 3)3 by hand and describe the end behavior

36. ## trig

Graph three periods of the function. (identify period and phase shift and intercepts) y = f(x) = √3/2 sin(2x) - 1/2 cos(2x) if you can't graph it can you at least get it into that simpler form which is graph able.

37. ## Math

Graph y=5^x and y=log_5 x on a sheet of paper using the same set of axes. Use the graph to describe the domain and range of each function. Then identify the y-intercept of each function and any asymptotes of each function

38. ## Algebra

1. In the formula S=a1(1−r), what restrictions are placed on the variable r? 2. The formula A=12bh can also be expressed as A=bh2. Do you agree? 3. If x and y are real numbers, and xy=0, then either x=0 or y=0. Do you agree? 4. Do the inequalities xlogx?

39. ## Math-due today, need a check

Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.

40. ## precalculus

analyzethe graph of the function Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (c) Find the maximum number of turning points. (d) Graph the function Please show

41. ## College alg

Analyze the graph of the following function as follows: (a) Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (c) Find the maximum number of turning points.

42. ## calculus

I have two questions, please help. 1. Uss completing the square to describe the graph of the following function. Support your answers graphically. f(x)= -2x^2+4x+7 please show work. 2. Can someone help me to graph this function? f(x)=x^2-6x+5 Then find the

43. ## Math

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

44. ## algebra 2

Graph the function f(x) = –3x^3 + 9x^2 – 2x + 3 using graphing technology and describe the end behavior

45. ## Algebra

Please Help Guys! 1) Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? A.The expression has a constant outside of the squared term. B. The expression is not the product of two binomials. C. The variable x has a coefficient. D. Some of the terms

46. ## algebra

list the domain and the x- and y- intercepts of the following function. Graph the funciion. Graph the function. Be sure to label all the asymptotes.

47. ## Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?

48. ## Algebra 2

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

49. ## Math2

Sketch the graph of this quadratic function: f(x)= 3(x-2)^2 -10. Be sure to explain the steps you take. **I don't need help with the graph part but I need to find the x and y intercepts, the equation of the axis of symmetry and the coordinates of the

50. ## math

Which three options are true about the quadratic equation?? y= 4t^2 + 16t + 18 A. The graph has a minimum. B. The graph of y crosses the horizontal axis at t = 10 and t = 20. C. The equation 4t^2 + 16 + 18 = 6 has one real solution. D. The function has a

51. ## algebra

2. The function f is defined as follows f(x)={4+2x if x0 a) Find the domain of the function b) Locate any intercepts c) Graph function d) Based on graph find range e) Is f continuous on its domain? a) The domain of the function f is

52. ## Algebra U4 L25

While performing a vertical line test on a graph, you notice that the graph intercepts the vertical line twice. Which of the following correctly interprets the result of the test? Because the vertical line intercepted the graph more than once, the graph is

53. ## Math

1. determine the interval(s) where the function f(x)= -1 / 2x+10 is a) positive b) Increasing 2. Consider the function f(x) = 3 / 4x-5 a) Determine the key features of the function: i) Domain and range ii)Intercepts iii) Equations of any asymptotes iv)

54. ## Math

4. Describe the behavior of the graph at the x-intercepts for the function f(x) = (2x-7)^7 (x+3)^4. Be sure to identify each x-intercept and justify your answer. How does each exponent change the look of the graph at the x-axis?

55. ## Calculus

Given the function f(x)= x√(x+3), Indicate the domain of f(x): ………………………… What are the x – intercepts of the graph of f(x)? POINTS! ……………………………. Identify the critical points of f(x) (write pairs of coordinates,

56. ## ALGEBRA

Create a rational function with a linear binomial in both the numerator and denominator. Part 1. Graph your function using technology. Include the horizontal and vertical asymptotes and the x- and y-intercepts on your graph. Label the asymptotes and

57. ## MATH TRIGONOMETRY

refer to the polynomial function f(x)= -x(x-1)(x+2) in anwering the folloowing questions. 1.what is the y intercept? 2.what is the behavior of the left end of its graph? 3.will the graph pass through the origin? 4,what is the behavior of the left end of

58. ## College Algebra

Using the 7 steps outlined in section 4.3 of your book, analyze the graph of the following function: R(x) = x^2 - 49/x^4 - 16 Step 1: Factor the numerator and denominator of R and find its domain. If 0 is in the domain, find y-intercept, R(0), and plot it.

59. ## Pre-Calculus

(I NEED URGENT HELP FOR THIS) Given the info. that a rational function has a vertical asymptote of x=3 and x=-3, horizontal asymptote at y=-4, no x-intercepts, and y-intercept: (0,2/3), no removable discontinuity, and no end behavior, what would the

60. ## Math

Describe the end behavior and estimate the x-and y-intercepts for each function. Estimate to the nearest tenth when necessary. y=-2x^5+x^3

61. ## Alg

describe the end behavior of the graph of the polynomial function. Then evaluate the ntion for x=-4, -3, -2, -1, 0, 1, 2, 3, 4. I'm confused on this. Help.

62. ## math, algebra,graphs help

THe directions state: (A)Complete the table, (B) describe the resulting graphs by identifying the vertex point, (C)the graph’s direction, (D) and any axis intercepts gleaned from the table or graph Problem #3 Equation : y = 2x^2 My answers: A) Table:

63. ## Algebra

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 how would I solve this?

64. ## mathematics

find the x-intercepts and y-intercepts of the function f(x)=x^2 +6x +9 and the graph function

65. ## limit from graph

How do I know if the limit of a function exists or not from that function's graph. Thanks. It the graph of a function becomes straighter at + and -infinity, it means that the function behaves linearly in the limit. However there may be other types of

66. ## College Algebra

1.The graph of y = - 1/2 |x - 5| - 3 can be obtained from the graph of y = |x| by which transformations? What is the horizontal shift? By what factor is the graph stretched or shrunk vertically and how is it reflected? What is the vertical shift? 2. Find

67. ## algebra

find the following for the function f(x)= (x+5)^2(x-1)^2 a) find the x and y intercepts for the polynomial function f b) determine whether the graph of f crosses or touches the x axis at each x intercept C) put all information together to obtain the graph

68. ## Math

Find the x- and y-intercepts and graph the equation plotting the intercepts. Please show all of your work. Submit your graph to the Dropbox 2x-3y=9

69. ## Algebra 2

These 3 equations all describe the same quadratic function. What are the coordinates of the following points on the graph of the function? From which equation is each point most easily determined? y = (x - 5) (x + 1) y = x^2 - 4x - 5 y = (x - 2) ^2 - 9

70. ## College algebra

Given the following quadratic equation find. a) the vertex b) the axis of symmetry c) the intercepts d) the domain e) the range f) the interval where the function is increasing g) the interval where the function is decreasing h) graph the function y=

Given the following quadratic equation find. a) the vertex b) the axis of symmetry c) the intercepts d) the domain e) the range f) the interval where the function is increasing g) the interval where the function is decreasing h) graph the function y=

72. ## math

Your friend runs up to you, scared that he is not ready for the upcoming quadratics test. To help him study, you will create four different quadratic functions. Then demonstrate to him how to rewrite each function as a group of factors, if possible. The

73. ## I need help with these please ALGEBRA

1. Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3 2. Evaluate : sqrt7x(sqrtx-7sqrt7) show your work. 3. Solve the equation. Check for

74. ## Calculus

Suppose f(x)= e^(-1/x). Graph this function in the window -5(

75. ## Calculus

Suppose f(x)= e^(-1/x). Graph this function in the window -5(

76. ## algebra II

Can you please help me with the these problems. 8.Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 11x^2, but which has its vertex at (2, 9). 10. Use the vertex and intercepts to sketch the graph of the

77. ## calculus II

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity?

78. ## math

Please help me! f(x)=(x+1)^3-2 1. How do I find the x and y intercepts, if any? 2. Describe the long term behavior of this function. Give the power function that F resembles.

79. ## math 11

4. a)how many different x-interceps could the graph of a quadratic function have? explain. it can have more than one because a parabola is a curved line on a graph in which case it touches two or more different points on the x-axis b)how many different

80. ## math

find the x-intercepts for P(x)= x^4-10x^2+9 and determine the behavior of the graph near the intercepts

81. ## Calculus

I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity?

82. ## graph of a polynomial

Sketch the graph of 1/12(x+2)^2(x-3)^2 and make sure the graph shows all intercepts and exhibits the proper end behavior. I can sketch the graph but how do I do the second part? Thanks What does the function do at x= inf, or x= -inf. That is the end

83. ## Math

Describe the end behavior and estimate the x-and y-intercepts for each function. Estimate to the nearest tenth when necessary. y+-2x^5+x^3

84. ## MATH

1.Graph the function f(x) = (x + 3)3 by hand and describe the end behavior.

find the slant asymptote of the graphof the rational function. 1.f(x)=x^2-x-2/x-7 y=? 2. determine the symmetry of the graph of f. a. the graph has y-axis symmetry f(-x)=f(x) b. the graph has orgin symmetry f(-x)= -f(x) c. the graph has both y-axs and

Please explain to me how to do the following problems, I don't understand them. Thanks! Find the x-intercepts (if any) for the graph of the quadratic function. 1.f(x) = (x + 2)2 - 4 Find the y-intercept for the graph of the quadratic function. 5.y + 9 = (x

87. ## Help !

Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term. -3x5 + 9x4 + 5x3 + 3

88. ## Pre-Calculus

1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x-6. 2) Use a graphing utility to graph the function and determine the x-intercepts and B. set y=0

89. ## Pre-Calculus

Radical Functions Graph y=(x-3)(x+2) and y=√(x-3)(x+2). where are the x-intercepts of each function ?why? for the first one, i know that whatever is inside the brackets is opposite, so the x intercepts would be at 3, and -2. but the whole radical thing

90. ## Pre-Calculus

Graphing Polynomials Decide whether each of the following is sometimes true, always true, or never true and explain reasoning. A. A cubic function has 2 different x-intercepts ^Never true, has to have 3? B. A cubic function has 3 x-intercepts ^ Always true

91. ## pre calculus

find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find the x and y intercept of the polynomial function f. b.)find the power function that the graph of f ressembles for large values of lxl. c.)determine the maximum number of turning pointsof the

92. ## Math

Find two quadratic functions whose graph have the given x-intercepts. Find one function whose graph opens upward and another whose graph open downdward. (-5/2,0),(-2,0)

1. a). Calculate (x^5+9x^4-3x^3+5x+8) / (x^2+3x+1) using long division. b). Write a division statement. 2. Calculate (-2x^4 +x^3-8x^2+11) / (x-6) using synthetic division. 3. Determine the domain, intercepts, asymptotes (if any), and positive/negative

94. ## College Algrbra

Given the following quadratic equation, find a. the vertex b. the axis of symmetry. the intercepts d. the domain e. the range f. the interval where the function is increasing, and g. the interval where the function is decreasing h. Graph the function

95. ## Algebra,Math, graphs help

This is what the directions state to do: (A) Complete the table,(B)describe the resulting graphs by identifying the vertex point, (c) the graph’s direction, (d) and any axis intercepts gleaned from the table or graph. Problem #1 Equation is : y = -x + 1

96. ## Pre cal

)a function f is defined as f(x) = 3*2^x describe the end behavior of f, please describe in detail how you got the answer and explain your abbreviations.

97. ## algebra2

What are the x-intercepts for the graph of the quadratic function f(x)=1/4(x +2)^2-9

98. ## Intermediate Algebra

Find the x- y-intercepts and graph the function f(x)=5x-10

99. ## Math/Algebra

Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.

100. ## Math

The distance d1 in miles, a small plane is from its final destination is given by d(t) = 250 – 100t, where t is the time, in hours, remaining for the flight. Find and discuss the meaning of the intercepts of the graph of the function. (You must first
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### Content Structure
The text passage is a collection of questions and problems related to graphing and analyzing polynomial functions, particularly focusing on quadratic functions. The questions cover various aspects such as finding x-intercepts, y-intercepts, vertex, axis of symmetry, and describing the end behavior of the functions.

### Analysis
TYPE: MULTIPLE_QUESTIONS

1. **Question 1:**
   - **Content:** Describe the behavior of the graph at the x-intercepts for the function \( f(x) = (2x-7)^7 (x+3)^4 \).
   - **Analysis:** This question asks for the behavior of the graph at the x-intercepts, which are \( x = \frac{7}{2} \) and \( x = -3 \). The behavior is determined by the exponents of the factors. At \( x = \frac{7}{2} \), the graph crosses the x-axis because the exponent is odd. At \( x = -3 \), the graph touches the x-axis and turns back because the exponent is even.

2. **Question 2:**
   - **Content:** What are the x-intercepts of the graph of the quadratic function \( f(x) = 5x^2