Question

1. $f(x)=|3x| + 2$; horizontal shrink by a factor of $\frac{1}{3}$

Explanation:

Step1: Recall transformation rule

For a function $y = f(x)$ and a horizontal shrink by a factor of $a$, the new function is $y = f(ax)$. Here $a = 3$ (since we are shrinking by a factor of $\frac{1}{3}$).

Step2: Substitute $ax$ into the function

Given $f(x)=\vert3x\vert + 2$, when we perform the horizontal - shrink, we replace $x$ with $3x$. So the new function $g(x)=f(3x)=\vert3(3x)\vert+2$.

Step3: Simplify the function

$g(x)=\vert9x\vert + 2$.

Answer:

$y=\vert9x\vert + 2$