# The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g: a) The graph of f(x)= absolute value of x is reflected about...

The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g:

a) The graph of f(x)= absolute value of x is reflected about the x-axis, vertically shrunk by a factor of .5, shifted 3 units to the right and shifted 2 units down.

b) The graph of f(x)= cube root of x is shifted four units to the left and two units down. For this one I got f(x)= (cube root of x +4) -2 .. is that correct?

Asked on by ceeee

rcmath | High School Teacher | (Level 1) Associate Educator

Posted on

A) When you reflect abs(x) about the x-axis, you end up with -abs(x).

Next let's pay attention to the fact that when yo multiply by 0.5 the graph actually expand and not shrink. So for it to shrink by half means to multiply by 2.
Shift to the right 3 means subtract 3 from x, and 2 up, you add 2 to the function. Thus we end up with

`y=2lx-3l+2` (that is 2*abs(x-3)+2)
The text passage contains a mathematical question with a request to find a transformed function based on a series of transformations applied to a given function. It also includes a proposed answer for one of the parts of the question.
multiple_questions_with_answers
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
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# The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g: a) The graph of f(x)= absolute value of x is reflected about...

The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g:

a) The graph of f(x)= absolute value of x is reflected about the x-axis, vertically shrunk by a factor of .5, shifted 3 units to the right and shifted 2 units down.

b) The graph of f(x)= cube root of x is shifted four units to the left and two units down. For this one I got f(x)= (cube root of x +4) -2 .. is that correct?

Asked on by ceeee

rcmath | High School Teacher | (Level 1) Associate Educator

Posted on

A) When you reflect abs(x) about the x-axis, you end up with -abs(x).

Next let's pay attention to the fact that when yo multiply by 0.5 the graph actually expand and not shrink. So for it to shrink by half means to multiply by 2.
Shift to the right 3 means subtract 3 from x, and 2 up, you add 2 to the function. Thus we end up with

`y=2lx-3l+2` (that is 2*abs(x-3)+2)
user
The text passage contains a mathematical question with a request to find a transformed function based on a series of transformations applied to a given function. It also includes a proposed answer for one of the parts of the question.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS