Question

Given that f(x) = | x | is the parent function and that g(x) is the parent function reflected over the y-axis and contains a horizontal shrink by a factor of 1/3. Which of the following functions represents g(x)?

Answer 1

In geometry, several transformations (such as dilation, rotation, reflection, etc.) can be applied to move a parent function to a new function. The function that represents g(x) is $g(x) = 3|x|$

Given that:

$f(x) = |x|$

First, we reflect over the y-axis.

The rule of this transformation is: $(x,y) \to (-x,y)$

So, the function becomes

$f'(x) = |-x|$

$f'(x) = |x|$

Next, shrink horizontally by 1/3

The rule of this transformation is: $(x,y) \to (\frac{x}{a},y)$

Where:

$a = \frac{1}{3}$

So, we have:

$g(x) = |\frac{x}{1/3}|$

$g(x) = |3x|$

$g(x) = 3|x|$

Hence, the function that represents g(x) is $g(x) = 3|x|$

Read more about function transformations at:

brainly.com/question/12865301