https://file.aiquickdraw.com/mathbot/file/1725999447477olzgu3y3.jpg

In the provided image, the function \( f(x) \) is graphed, and there are two tasks shown:

1. **Evaluate \( f(2) \):**
   - From the graph, when \( x = 2 \), the function value \( f(2) = 4 \). This part is correctly answered.

2. **Solve \( f(x) = 2 \):**
   - To find where \( f(x) = 2 \), look for the point(s) where the function intersects the line \( y = 2 \). From the graph, the function intersects the horizontal line \( y = 2 \) at approximately \( x = -1 \). Therefore, the correct solution should be \( x = -1 \), not \( x = -4 \).

Would you like further explanation on this? Here are some related questions to deepen your understanding:

1. What does it mean when a function intersects a specific line, like \( y = 2 \)?
2. How can you verify solutions by substituting back into the function?
3. What are the common methods to solve equations involving functions graphically?
4. Can you describe what happens to the value of \( f(x) \) as \( x \) increases for this graph?
5. How do you find other key points on the graph, such as intercepts or turning points?

**Tip:** When solving equations graphically, always double-check the points of intersection visually or by using a ruler for more accuracy.

Evaluate f(2) and solve f(x) = 2 based on the graph of the function f(x).

This problem involves analyzing a graph to evaluate the function f(x) at specific points. It includes evaluating f(2) from the graph and solving for x when f(x) = 2 by identifying the intersection point on the graph. Suitable for students in Grades 9-12.

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