Question

evaluate: $f(g(0))$
$y = f(x)$
$y = g(x)$

Explanation:

Step1: Find \( g(0) \)

To find \( g(0) \), we look at the graph of \( y = g(x) \) and find the \( y \)-value when \( x = 0 \). From the graph of \( y = g(x) \), when \( x = 0 \), \( g(0)=1 \).

Step2: Find \( f(g(0)) = f(1) \)

Now we need to find \( f(1) \) using the graph of \( y = f(x) \). The graph of \( y = f(x) \) is a line. We can use the slope - intercept form or just read the value. The equation of the line \( y = f(x) \) can be found. We know two points: when \( x = 0 \), \( y=- 3\) (from the graph \( y = f(x) \) passes through \( (0,-3) \)) and when \( x = 3 \), \( y = 0 \) (since it crosses the \( x \)-axis at \( (3,0) \)). The slope \( m=\frac{0 - (-3)}{3-0}=\frac{3}{3} = 1 \). So the equation is \( y=x - 3 \). When \( x = 1 \), \( y=1-3=-2 \). Alternatively, by looking at the graph of \( y = f(x) \), when \( x = 1 \), we can see that \( f(1)=1 - 3=-2 \).

Answer:

\(-2\)