Question

select the correct answer.
if the graph of $f(x) = |x|$ is compressed vertically by a factor of $\frac{1}{3}$ and shifted 3 units to the right, which function represents the new graph?

• $g(x) = |\frac{1}{3}x| - 3$
• $g(x) = |\frac{1}{3}x| + 3$
• $g(x) = \frac{1}{3}|x + 3|$
• $g(x) = \frac{1}{3}|x - 3|$

Explanation:

Step1: Vertical compression by $\frac{1}{3}$

Multiply the original function by $\frac{1}{3}$: $\frac{1}{3}|x|$

Step2: Shift 3 units to the right

Replace $x$ with $x-3$ in the function: $\frac{1}{3}|x-3|$

Answer:

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