Let's solve the two function composition problems from the graph step by step.

1. $f(g(0))$

First, let's find $g(0)$:

• Looking at the graph of $g(x)$, when $x = 0$, we can see that $g(0) = 1$.

Now, we need to find $f(g(0))$, which is $f(1)$:

• From the graph of $f(x)$, when $x = 1$, we can see that $f(1) = 1$.

So, $f(g(0)) = 1$.

2. $g(f(-5))$

First, let's find $f(-5)$:

• Looking at the graph of $f(x)$, when $x = -5$, we can see that $f(-5) = 3$.

Now, we need to find $g(f(-5))$, which is $g(3)$:

• From the graph of $g(x)$, when $x = 3$, we can see that $g(3) = -3$.

So, $g(f(-5)) = -3$.

Final answers:

• $f(g(0)) = 1$
• $g(f(-5)) = -3$

Would you like more details on how to interpret these graphs or the composition of functions? Here are some related questions for further practice:

1. What is $f(g(2))$?
2. What is $g(f(0))$?
3. What is $f(g(-3))$?
4. How does the graph of a composition $f(g(x))$ look compared to $f(x)$ and $g(x)$?
5. Can function compositions always be evaluated using graphs?

Tip: When dealing with function compositions, always work from the inside out—evaluate the innermost function first, then proceed outward.