Question

write a formula for the function g that relates when the graph of f(x) is transformed as described. the graph of f(x)=|x| reflected over the y - axis and horizontally compressed by a factor of 1/3. select one: a. g(x)=|-3x|. b. g(x)=| - (1/3)x |. c. g(x)=|3x|. d. g(x)=-|3x|.

Explanation:

Step1: Reflect over y-axis

Replace $x$ with $-x$ in $f(x)$:
$f(-x) = |-x|$
Since $|-x|=|x|$, this simplifies to $|x|$.

Step2: Horizontal compression by $\frac{1}{3}$

Replace $x$ with $3x$ (for horizontal compression by factor $\frac{1}{a}$, use $ax$):
$g(x) = |-3x|$
Note that $|-3x|=|3x|$, so this can also be written as $|3x|$.

Answer:

A. $g(x) = | - 3x|$, C. $g(x) = |3x|$