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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.

Given the table and graph, determine (f ∘ g)(0) and (f ∘ g)(1).

Learn how to solve function composition problems such as (f ∘ g)(0) and (f ∘ g)(1) using a graph and a table. This example covers essential concepts in algebra, including function composition and graph interpretation, suitable for Grades 9-11.

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