https://file.aiquickdraw.com/mathbot/file/1729397071353ul0h81y5.jpg

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.

Use the graphs for f(x) and g(x) to evaluate the expressions below: f(g(0)) and g(f(-5)). Write your answer as an integer or a reduced fraction.

Learn how to evaluate function compositions f(g(0)) and g(f(-5)) using given graphs of f(x) and g(x). This problem focuses on interpreting graphs for function values and composing functions. Suitable for high school students in Grades 9-12.

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