Question

what is the equation for g(x)? function g can be thought of as a scaled version of f(x)=|x|.

Explanation:

Step1: Recall the form of absolute - value function

The general form of an absolute - value function is $y = a|x|$, where $a$ is a scalar.

Step2: Identify a point on $g(x)$

The graph of $y = f(x)=|x|$ passes through $(1,1)$ and $(- 1,1)$. For the function $g(x)$, when $x=-2$, $y = 1$.

Step3: Find the value of $a$

Substitute $x=-2$ and $y = 1$ into $y=a|x|$. We get $1=a|-2|$, so $1 = 2a$. Solving for $a$, we have $a=\frac{1}{2}$.

Answer:

$g(x)=\frac{1}{2}|x|$