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To graph \( h(x) = (f + g)(x) \), we need to add the corresponding values of the functions \( f(x) \) and \( g(x) \) at each \( x \)-coordinate and plot the resulting points. Let's analyze the graphs step-by-step.

### Step 1: Identify key points for \( f(x) \) and \( g(x) \)

For function \( f(x) \) (top graph):
- \( f(-3) = 0 \)
- \( f(-2) = 2 \)
- \( f(0) = 3 \)
- \( f(2) = 2 \)
- \( f(3) = 0 \)

For function \( g(x) \) (bottom graph):
- \( g(-3) = -3 \)
- \( g(-2) = 0 \)
- \( g(0) = -1 \)
- \( g(2) = 1 \)
- \( g(3) = 2 \)

### Step 2: Compute \( h(x) = f(x) + g(x) \) for each \( x \)-value
- \( h(-3) = f(-3) + g(-3) = 0 + (-3) = -3 \)
- \( h(-2) = f(-2) + g(-2) = 2 + 0 = 2 \)
- \( h(0) = f(0) + g(0) = 3 + (-1) = 2 \)
- \( h(2) = f(2) + g(2) = 2 + 1 = 3 \)
- \( h(3) = f(3) + g(3) = 0 + 2 = 2 \)

### Step 3: Plot the points for \( h(x) \)
You need to plot the points:
- \( (-3, -3) \)
- \( (-2, 2) \)
- \( (0, 2) \)
- \( (2, 3) \)
- \( (3, 2) \)

After plotting these points, connect them with line segments to complete the graph of \( h(x) \).

Would you like further details on how to graph this, or help with any other part?

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Here are 5 related questions to expand on this topic:
1. How do you determine the domain and range of \( h(x) \)?
2. What happens when you subtract two functions instead of adding them?
3. Can you interpret the meaning of the intersection points between \( f(x) \) and \( g(x) \)?
4. What would the graph look like if \( f(x) \) were multiplied by a scalar before adding to \( g(x) \)?
5. How do transformations (like shifting or stretching) affect the sum of two functions?

**Tip:** When graphing, it can help to use a table of values to ensure accuracy before drawing the segments.

Use the graphs of f and g to graph h(x) = (f + g)(x).

Learn how to graph the sum of two functions, f(x) and g(x), by adding their corresponding values at key points. This problem demonstrates graphing skills and the concept of function addition, suitable for Grades 9-12.

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