Question

what is the equation for $g(x)$?
choose 1 answer:
a $g(x) = \frac{3}{2}|x|$
b $g(x) = -\frac{2}{3}|x|$

Explanation:

Step1: Analyze the graph of \( g(x) \)

The graph of \( g(x) \) is a dashed line, and it has a negative slope (since it goes from the second quadrant to the fourth quadrant), so the coefficient of \( |x| \) should be negative. This eliminates option A.

Step2: Check the slope

Let's take a point on \( g(x) \). For example, when \( x = 3 \), from the graph, we can see that \( y=-2 \) (approximate). Let's test option B: \( g(3)=-\frac{2}{3}|3| = -\frac{2}{3}\times3=-2 \), which matches the point.

Answer:

B. \( g(x) = -\frac{2}{3}|x| \)