Question

function g can be thought of as a scaled version of f(x)=|x|. what is the equation for g(x)? choose 1 answer: a g(x)=|x + 0.2| b g(x)=|x - 0.2| c g(x)=-0.2|x| d g(x)=0.2|x|

Explanation:

Step1: Identify transformation type

The graph of $g(x)$ is a vertical scaling and reflection of $f(x)=|x|$ (it opens downward and is narrower/wider than $f(x)$).

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

Take $x=5$: from the graph, $g(5)=-1$. Substitute into options:

• Option A: $|5+0.2|=5.2

eq-1$

• Option B: $|5-0.2|=4.8

eq-1$

• Option C: $-0.2|5|=-0.2\times5=-1$, which matches
• Option D: $0.2|5|=1

eq-1$

Step3: Confirm scaling/reflection

A negative coefficient reflects over the x-axis, and $0.2$ scales the function vertically. This matches the downward-opening, compressed shape of $g(x)$.

Answer:

C. $g(x) = -0.2|x|$