Question

evaluate: $g(f(-5))$
$y = f(x)$ (graph of a parabola) and $y = g(x)$ (graph of a piecewise linear function)

Explanation:

Step1: Find \( f(-5) \) from \( y = f(x) \)

Looking at the graph of \( y = f(x) \), when \( x = -5 \), we find the corresponding \( y \)-value. From the parabola, at \( x = -5 \), the \( y \)-coordinate is \( -8 \). So \( f(-5) = -8 \).

Step2: Find \( g(f(-5)) = g(-8) \) from \( y = g(x) \)

Now we need to find \( g(-8) \) using the graph of \( y = g(x) \). Looking at the graph of \( y = g(x) \), we find the \( y \)-value when \( x = -8 \). From the piece - wise linear graph, when \( x=-8 \), we can see that the \( y \)-coordinate is \( 1 \) (by following the left - hand line of the piece - wise function: the left part of \( y = g(x) \) has a slope, and when \( x=-8 \), we can calculate or directly read from the graph. The left line passes through points, for example, when \( x=-7 \), let's check the pattern. But directly from the graph, when \( x = -8 \), the \( y \)-value is \( 1 \)). So \( g(-8)=1 \).

Answer:

\( 1 \)