To solve the problem, we need to determine the values of $(f \circ g)(0)$ and $(f \circ g)(1)$ using the provided table and graph. The function composition $(f \circ g)(x)$ means $f(g(x))$.

Step 1: Determine $g(0)$ and $g(1)$ from the table.

From the table:

• $g(0) = -4$
• $g(1) = 2$

Step 2: Use the graph to find $f(g(0))$ and $f(g(1))$.

Using the graph:

1. For $x = g(0) = -4$:

   • Locate $x = -4$ on the graph.
   • From the graph, when $x = -4$, $f(-4)$ is approximately 5.

   Therefore, $f(g(0)) = f(-4) = 5$.

2. For $x = g(1) = 2$:

   • Locate $x = 2$ on the graph.
   • From the graph, when $x = 2$, $f(2) = -2$.

   Therefore, $f(g(1)) = f(2) = -2$.

Final Answers:

• $(f \circ g)(0) = 5$
• $(f \circ g)(1) = -2$

Would you like any further details or have any questions?

Here are some related questions for further practice:

1. What is $(g \circ f)(1)$ based on the graph and table?
2. How does changing the value of $g(x)$ affect the composition $f(g(x))$?
3. What would $(f \circ g)(2)$ be using the same functions?
4. Explain how to interpret the graph of $f(x)$ for different values of $x$.
5. Can function compositions be used to solve real-world problems? Provide an example.

Tip: When dealing with function compositions, always evaluate the inner function first before applying the outer function.