Pre Calculas

Im really struggling and need help with this
1. One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the

Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43

Table #2 x 1 2 3 4 5 6 7 y 10 13 18 21 26 29 34

Table #3 x 2 4 6 8 10 12 14 y 1 6 11 16 21 26 31

2. Give an example of each of the following:

A function whose domain is [2, infinity)
An arithmetic sequence
A system of equations with no solutions

3. For f(x) = 1/x^2-3, find:

f(3)
f(2+h)
4. For f(x) = 1/x-5 and g(x) = x^2+2, find:
1. (fog)(x)
2. (gof)(6)
5. For the sequence given by a (subscript n) = 4n+5 an=4n+5, answer the following:

Find the first five terms
Find the sum of the first 25 terms.
Is this an arithmetic sequence? If so, how can you tell? If not, why not?
6. Graph the area bound by y<1/2x+6, x+3y>=12, x>=0, and x<=12
7. For the function defined by:
f(x)= {x^2, x<=1}
{2x+1, x>1}
a. evaluate f(0)
b. graph f(x)
8. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices.
3x-y=0
5x+2y=22
9. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices
8x-2y=5
-12x+3y=7
10.Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why.
A (3x3) [1st 2, -1, 0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]
B (3x3) [1st 5, 0, 2] [2nd 1, -3, 9] [3rd2, 0, 4]
C (1x1) [1, 3, 5]
1.3A+B
2. B+C
3. CA
11. Given the table below, evaluate the following:

x

-3

-2

-1

0

1

2

3

4

5

f(x)

10

20

30

40

50

60

70

80

90

g(x)

-1

-2

-3

-4

-5

-6

-7

-8

-9

a. (3f+2g(1) b. (fog)(-1)
12. Express the following function, F(x) as a composition of two functions f and g
f(x)= x^2/(x^2+4)
13. You have a coupon for your favorite clothing store for \$25 off any purchase of more than \$50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the \$25 coupon applied, and g(x) be the price with the 20% discount applied.
a. Write an expression for f(x)
b. Write an expression for g(x)
c. What would the expression (fog)(x) represent?
d. What would the expression (gof)(x) represent?
e. If the store allows you to apply both the 20% discount and the \$25-off coupon, does it matter which you apply first? How do you know?

1. 👍
2. 👎
3. 👁
1. #1 in a linear function, equal spacing in x produces equal spacing in y. The ratio is called the slope, and is constant. Only table #3 meets that condition.

#2
A function whose domain is [2, infinity): √(x-2)
An arithmetic sequence: 1,2,3,4,...
A system of equations with no solutions:
x+y=1
x+y=2

#3
f(x) = 1/(x^2-3), find:
f(3) = 1/(3^2-3) = 1/6
f(2+h) = 1/((2+h)^2-3) = 1/(h^2+4h-1)

#4
f(x) = 1/x-5 and g(x) = x^2+2, find:
1. (fog)(x) = f(g(x)) = 1/(g-5) = 1/(x^2+2-5) = 1/(x^2-3)
2. (gof)(6) = g(f(6)) = g(1) = 1^2+2 = 3

#5
Find the first five terms: 9,13,17,21,25
Find the sum of the first 25 terms: (25/2)(2*9+24*4) = 1425
Is this an arithmetic sequence? Yes, because A_n+1 - A_n = 4(n+1)+5 - (4n+5) = 4, a constant

1. 👍
2. 👎
2. Thanks Steve for the help

1. 👍
2. 👎

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The text passage contains multiple mathematical questions and problems, ranging from identifying linear functions from tables to solving systems of equations and working with functions and sequences.
multiple_questions
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
Pre Calculas

Im really struggling and need help with this
1. One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the

Table #1 x 2 5 8 11 14 17 20 y 1 3 7 13 21 31 43

Table #2 x 1 2 3 4 5 6 7 y 10 13 18 21 26 29 34

Table #3 x 2 4 6 8 10 12 14 y 1 6 11 16 21 26 31

2. Give an example of each of the following:

A function whose domain is [2, infinity)
An arithmetic sequence
A system of equations with no solutions

3. For f(x) = 1/x^2-3, find:

f(3)
f(2+h)
4. For f(x) = 1/x-5 and g(x) = x^2+2, find:
1. (fog)(x)
2. (gof)(6)
5. For the sequence given by a (subscript n) = 4n+5 an=4n+5, answer the following:

Find the first five terms
Find the sum of the first 25 terms.
Is this an arithmetic sequence? If so, how can you tell? If not, why not?
6. Graph the area bound by y<1/2x+6, x+3y>=12, x>=0, and x<=12
7. For the function defined by:
f(x)= {x^2, x<=1}
{2x+1, x>1}
a. evaluate f(0)
b. graph f(x)
8. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices.
3x-y=0
5x+2y=22
9. Solve the following system of equations algebraically. Verify your solution either graphically or by using matrices
8x-2y=5
-12x+3y=7
10.Given matrices A, B, and C below, perform the indicated operations if possible. If the operation is not possible, explain why.
A (3x3) [1st 2, -1, 0] [2nd 0, 5, 0.3] [3rd 1, 4, 10]
B (3x3) [1st 5, 0, 2] [2nd 1, -3, 9] [3rd2, 0, 4]
C (1x1) [1, 3, 5]
1.3A+B
2. B+C
3. CA
11. Given the table below, evaluate the following:

x

-3

-2

-1

0

1

2

3

4

5

f(x)

10

20

30

40

50

60

70

80

90

g(x)

-1

-2

-3

-4

-5

-6

-7

-8

-9

a. (3f+2g(1) b. (fog)(-1)
12. Express the following function, F(x) as a composition of two functions f and g
f(x)= x^2/(x^2+4)
13. You have a coupon for your favorite clothing store for \$25 off any purchase of more than \$50. The store is also running a 20%-off sale on its entire inventory. Let x be the original price, f(x) be the price with the \$25 coupon applied, and g(x) be the price with the 20% discount applied.
a. Write an expression for f(x)
b. Write an expression for g(x)
c. What would the expression (fog)(x) represent?
d. What would the expression (gof)(x) represent?
e. If the store allows you to apply both the 20% discount and the \$25-off coupon, does it matter which you apply first? How do you know?

1. 👍
2. 👎
3. 👁
1. #1 in a linear function, equal spacing in x produces equal spacing in y. The ratio is called the slope, and is constant. Only table #3 meets that condition.

#2
A function whose domain is [2, infinity): √(x-2)
An arithmetic sequence: 1,2,3,4,...
A system of equations with no solutions:
x+y=1
x+y=2

#3
f(x) = 1/(x^2-3), find:
f(3) = 1/(3^2-3) = 1/6
f(2+h) = 1/((2+h)^2-3) = 1/(h^2+4h-1)

#4
f(x) = 1/x-5 and g(x) = x^2+2, find:
1. (fog)(x) = f(g(x)) = 1/(g-5) = 1/(x^2+2-5) = 1/(x^2-3)
2. (gof)(6) = g(f(6)) = g(1) = 1^2+2 = 3

#5
Find the first five terms: 9,13,17,21,25
Find the sum of the first 25 terms: (25/2)(2*9+24*4) = 1425
Is this an arithmetic sequence? Yes, because A_n+1 - A_n = 4(n+1)+5 - (4n+5) = 4, a constant

1. 👍
2. 👎
2. Thanks Steve for the help

1. 👍
2. 👎

Similar Questions

The Eatery Restaurant has 200 tables. On a recent evening, there were reservations for 1/10 of the tables. How many tables were reserved?

2. mathematics

it takes 12 men to make 12 tables in 9 hours. how long will it take 8 men to make 32 tables?

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Betty has the option of using three types of tables in her coffee shop: square tables with a side length of 42 inches; rectangular tables 26 inches wide and 73 2/3 inches long; and round tables with a diameter of 36 inches. Which

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A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 5 tables is \$43. The total cost to rent 8 chairs and 3 tables is \$36. What is the cost to rent each chair and each table?

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Franklin Furniture Company sells chairs for \$110 each and tables for \$322 each. Last month the company sold 65 items for a total of \$12,450. How many chairs and how many tables did they sell?

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How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? A. They help us to measure or estimate of the likelihood of a certain statistic falling within
user
The text passage contains multiple mathematical questions and problems, ranging from identifying linear functions from tables to solving systems of equations and working with functions and sequences.

TYPE: MULTIPLE_QUESTIONS