https://file.aiquickdraw.com/mathbot/file/1730295363357f1hgip08.jpg

To determine \( f(2) \) from the graph, let's analyze the function step-by-step.

1. **Identify the Type of Function**:
   The graph shows a straight line, indicating a linear function of the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

2. **Find the Slope (\( m \))**:
   To find the slope, choose two points on the line:
   - Point 1: \( (0, -2) \) (y-intercept)
   - Point 2: \( (2, 2) \)

   The slope \( m \) is calculated as:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-2)}{2 - 0} = \frac{4}{2} = 2
   \]

   So, the equation of the line becomes:
   \[
   f(x) = 2x - 2
   \]

3. **Calculate \( f(2) \)**:
   Substitute \( x = 2 \) into the function:
   \[
   f(2) = 2(2) - 2 = 4 - 2 = 2
   \]

### Answer:
\[
f(2) = 2
\]

Would you like further details on any step, or have other questions?

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Here are some related questions for deeper understanding:
1. How would we find \( f(x) \) if the slope was different?
2. What if the y-intercept was at a different point on the graph?
3. Can we find the equation of a line given only the slope and one point?
4. How would the function change if it had a negative slope?
5. What is the interpretation of slope in the context of a linear function?

**Tip**: For linear equations, always check the slope and intercept first to simplify your calculations!

The graph of a function is shown. What is f(2)?

Learn how to find f(2) from a linear function graph by calculating the slope and y-intercept. Suitable for Grades 7-9, this solution explains the use of slope formula and linear equation concepts.

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