https://file.aiquickdraw.com/mathbot/file/1734048276826nwwbzm28.jpg

Let's analyze the problem step by step.

### Problem Breakdown:
1. **Question (a):** Find one \( x \)-value for which \( f(x) = 4 \).
   - Look for where the graph has a \( y \)-coordinate of \( 4 \).
   - Locate the corresponding \( x \)-coordinate.

2. **Question (b):** Find \( f(-2) \).
   - Locate \( x = -2 \) on the graph.
   - Find the \( y \)-coordinate of the function at this \( x \)-value.

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### Solution:
#### (a) Finding \( x \) such that \( f(x) = 4 \):
From the graph:
- \( f(x) = 4 \) occurs where the horizontal line \( y = 4 \) intersects the function. 
- Looking at the graph, this happens at \( x = -3 \).

Thus, one value of \( x \) for which \( f(x) = 4 \) is:
\[
x = -3
\]

#### (b) Finding \( f(-2) \):
From the graph:
- At \( x = -2 \), the \( y \)-coordinate is \( 3 \).

Thus:
\[
f(-2) = 3
\]

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### Final Answers:
(a) \( x = -3 \)  
(b) \( f(-2) = 3 \)

Let me know if you need further clarification or want to go over details!

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### Additional Questions for Exploration:
1. What is the slope of the line represented by the function \( f(x) \)?
2. Can you determine the equation of the function \( f(x) \)?
3. What happens to \( f(x) \) as \( x \to \infty \)?
4. Can you find \( x \) such that \( f(x) = 0 \)?
5. What is \( f(0) \), and why?

**Tip:** Always identify key points (e.g., intercepts, specific values) to understand the behavior of a graph better.

The graph of a function f is shown below. Find one value of x for which f(x) = 4 and find f(-2).

Learn how to find the x-value for which f(x) = 4 and determine f(-2) using a linear function graph. Explore graph interpretation techniques, suitable for middle school students (Grades 6-8).

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