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 $g(x)=2|x|$
b $g(x)=-2|x|$
c $g(x)=\frac{1}{2}|x|$
d $g(x)=-\frac{1}{2}|x|$

Explanation:

Step1: Analyze the direction of the graph

The graph of \( g(x) \) is in the same direction (both arms going up) as \( f(x)=|x| \), so there is no reflection (the coefficient of \( |x| \) is positive). So we can eliminate options B and D.

Step2: Analyze the vertical scaling

For \( f(x) = |x| \), when \( x = 2 \), \( f(2)=|2| = 2 \). For \( g(x) \), when \( x = 2 \), from the graph, \( g(2) \) should be 1 (since it's a scaled version and the dashed line is less steep). Let's check the remaining options (A and C).

For option A: \( g(2)=2|2| = 4 \), which is not 1.

For option C: \( g(2)=\frac{1}{2}|2|=\frac{1}{2}\times2 = 1 \), which matches the expected value from the graph.

Answer:

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