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 [tex]g(x) = 3|x|[/tex]
Given that:
[tex]f(x) = |x|[/tex]
First, we reflect over the y-axis.
The rule of this transformation is: [tex](x,y) \to (-x,y)[/tex]
So, the function becomes
[tex]f'(x) = |-x|[/tex]
[tex]f'(x) = |x|[/tex]
Next, shrink horizontally by 1/3
The rule of this transformation is: [tex](x,y) \to (\frac{x}{a},y)[/tex]
Where:
[tex]a = \frac{1}{3}[/tex]
So, we have:
[tex]g(x) = |\frac{x}{1/3}|[/tex]
[tex]g(x) = |3x|[/tex]
[tex]g(x) = 3|x|[/tex]
Hence, the function that represents g(x) is [tex]g(x) = 3|x|[/tex]
Read more about function transformations at:
https://brainly.com/question/12865301
