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This image contains a graph with two functions, \( f(x) \) and \( g(x) \), and four sub-problems asking you to evaluate expressions involving these functions at given points. Here's the breakdown:

We need to use the graph to find specific values of \( f(x) \) and \( g(x) \) at certain points, then evaluate the given expressions.

### Step-by-step Solution:
1. **Find values from the graph:**
   - For \( x = 1 \), look at the graph for both \( f(x) \) and \( g(x) \):
     - \( f(1) \) is the y-value of the curve representing \( f(x) \) at \( x = 1 \).
     - \( g(1) \) is the y-value of the curve representing \( g(x) \) at \( x = 1 \).
   - For \( x = 0 \), locate the values of \( f(0) \) and \( g(0) \) on the graph.
   - For \( x = -1 \), locate \( f(-1) \) and \( g(-1) \).

2. **Evaluate each expression:**
   - **(a) \( (f + g)(1) \):**
     This means \( f(1) + g(1) \). Look at the graph for the values of \( f(1) \) and \( g(1) \) and sum them.
   - **(b) \( (f - g)(0) \):**
     This is \( f(0) - g(0) \). Find the values from the graph and subtract \( g(0) \) from \( f(0) \).
   - **(c) \( f(g(-1)) \):**
     First, find \( g(-1) \) from the graph, then substitute that value into \( f(x) \), meaning find \( f(g(-1)) \).
   - **(d) \( \left( \frac{f}{g} \right)(1) \):**
     This represents \( \frac{f(1)}{g(1)} \). Find the values from the graph and calculate the ratio.

### Detailed Calculation:
Please give me a moment to extract the necessary values from the graph.

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For \( f(x) \):
- \( f(1) \approx 2 \)
- \( f(0) \approx -2 \)
- \( f(-1) \approx 2 \)

For \( g(x) \):
- \( g(1) \approx 0 \)
- \( g(0) \approx 2 \)
- \( g(-1) \approx -2 \)

### Now let's compute:

(a) \( (f + g)(1) = f(1) + g(1) = 2 + 0 = 2 \)

(b) \( (f - g)(0) = f(0) - g(0) = -2 - 2 = -4 \)

(c) \( f(g(-1)) = f(-2) \)
   From the graph, \( f(-2) \approx -4 \), so \( f(g(-1)) = -4 \)

(d) \( \left( \frac{f}{g} \right)(1) = \frac{f(1)}{g(1)} = \frac{2}{0} \), which is undefined because division by zero is not possible.

### Final Answers:
- (a) 2
- (b) -4
- (c) -4
- (d) Undefined

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Would you like more details on any of the steps or further clarification? Here are some related questions:

1. How can we evaluate compositions of functions like \( f(g(x)) \)?
2. What happens when division by zero occurs in a function?
3. How do we interpret the difference between two functions, \( (f - g)(x) \)?
4. How can we apply the sum of functions graphically?
5. How do undefined values impact the domain of a function?

**Tip:** When interpreting a graph, ensure to accurately trace the corresponding y-value for the given x-coordinate to avoid mistakes.

Use the graph to evaluate the expression.

Learn how to evaluate function expressions based on a graph. This problem covers function addition, subtraction, composition, and division, with a step-by-step breakdown using graphical values. Suitable for students in Grades 10-12.

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