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The image contains a table and a graph. The table appears to list values of an affine function \( f(x) \), where specific values of \( x \) correspond to \( f(x) \). The graph seems to represent this function.

Let me describe the key points:

- The table shows values of \( f(x) \) for various \( x \):
  - \( x = 0 \), \( f(x) = 6 \)
  - \( x = 1 \), \( f(x) = 4 \)
  - \( x = 3 \), \( f(x) = 0 \)
  - \( x = 5 \), \( f(x) = -4 \)
  - \( x = 7 \), \( f(x) = -8 \)

- The graph visually represents this function, with points plotted according to the data from the table. It appears to show a straight line, consistent with the affine function form \( f(x) = ax + b \).

### Analysis of the Function:
The points given are linear, so the function follows the form:
\[
f(x) = mx + b
\]
To determine the slope \( m \), we can use two points. For example, using \( (0, 6) \) and \( (3, 0) \):
\[
m = \frac{0 - 6}{3 - 0} = \frac{-6}{3} = -2
\]
Now, we use the slope-intercept form to write the function:
\[
f(x) = -2x + 6
\]

This is the equation of the function.

### Do you have any questions about this? Here are 5 related questions to think about:

1. How would you calculate the slope if the points were not evenly spaced?
2. What is the significance of the \( y \)-intercept in this equation?
3. How can you verify that all points satisfy the equation \( f(x) = -2x + 6 \)?
4. How would the graph change if the slope were positive?
5. What happens to the graph if you shift the function vertically by adding a constant?

**Tip:** When working with affine functions, plotting a few points and calculating the slope can help visualize and confirm the equation.

The table and graph display values of a linear function f(x) and show that the function follows an affine form f(x) = ax + b.

This problem shows how to graph the linear function f(x) = -2x + 6 using a table of values. Learn how to calculate the slope using the formula m = (y2 - y1) / (x2 - x1) and analyze the graph. Suitable for students in Grades 9-11.

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