Question

which statement is true regarding the functions on the graph?
f(2) = g(2)
f(0) = g(0)
f(2) = g(0)
f(0) = g(2)

Explanation:

Step1: Analyze \( f(0) \) and \( g(0) \)

For \( f(x) \) (blue line), when \( x = 0 \), the \( y \)-value (from the graph) is 2, so \( f(0)=2 \). For \( g(x) \) (red line), when \( x = 0 \), the \( y \)-value is -2, so \( g(0)= - 2 \). So \( f(0)
eq g(0) \).

Step2: Analyze \( f(2) \) and \( g(2) \)

From the graph, both \( f(x) \) and \( g(x) \) intersect at \( x = 2 \), and the \( y \)-value at \( x = 2 \) for both is 0. So \( f(2)=0 \) and \( g(2)=0 \), thus \( f(2)=g(2) \).

Step3: Analyze \( f(2) \) and \( g(0) \)

We know \( f(2) = 0 \) and \( g(0)=-2 \), so \( f(2)
eq g(0) \).

Step4: Analyze \( f(0) \) and \( g(2) \)

We know \( f(0)=2 \) and \( g(2)=0 \), so \( f(0)
eq g(2) \).

Answer:

\( f(2) = g(2) \)