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The problem involves the functions \( f(x) \) and \( g(x) \) shown in the graphs and the expression \( h(x) = \frac{f(x) + g(x)}{x + 2} \). You are asked to find the value of \( h(2) \).

### Step 1: Evaluate \( f(2) \) and \( g(2) \)
First, we need to find the values of \( f(2) \) and \( g(2) \) from the graphs:

- **Graph of \( f(x) \):** At \( x = 2 \), the graph of \( f(x) \) shows that \( f(2) = 4 \).
- **Graph of \( g(x) \):** At \( x = 2 \), the graph of \( g(x) \) shows that \( g(2) = 6 \).

### Step 2: Plug in these values into the formula for \( h(x) \)
Now, substitute \( x = 2 \), \( f(2) = 4 \), and \( g(2) = 6 \) into the expression for \( h(x) \):

\[
h(2) = \frac{f(2) + g(2)}{2 + 2} = \frac{4 + 6}{4} = \frac{10}{4} = \frac{5}{2}
\]

### Step 3: Compare with answer choices
The value \( \frac{5}{2} \) corresponds to choice (A) in the provided answer choices.

**Answer: (A) \( \frac{5}{2} \)**

Would you like more details, or do you have any questions about this problem?

### Related Questions:
1. How do you find the value of a function at a specific point from its graph?
2. What is the importance of the denominator \( x + 2 \) in the expression for \( h(x) \)?
3. How would the solution change if \( x \) were a different value, such as \( x = 1 \)?
4. Can you explain the significance of each graph’s slope at \( x = 2 \)?
5. How can you determine if \( h(x) \) is increasing or decreasing at \( x = 2 \)?

**Tip:** Always check the units on the axes of the graph to ensure you interpret the function values correctly.

The graphs of the functions f and g are shown above. If h(x) = (f(x) + g(x)) / (x + 2), then h(2) = ?

Learn how to calculate h(2) using the graphs of the functions f(x) and g(x) and the algebraic formula h(x) = (f(x) + g(x)) / (x + 2). Suitable for high school students in Grades 10-12.

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