To complete the problem, follow these steps:

Step 1: Evaluate $f(x) = -2x + 6$ for the given values of $x$:

1. For $x = -2$: $f(-2) = -2(-2) + 6 = 4 + 6 = 10$ So, $f(-2) = 10$.

2. For $x = 0$: $f(0) = -2(0) + 6 = 0 + 6 = 6$ So, $f(0) = 6$.

3. For $x = 2$: $f(2) = -2(2) + 6 = -4 + 6 = 2$ So, $f(2) = 2$.

Step 2: Complete the table:

Step 3: Plot these points on the graph:

• Point 1: $(-2, 10)$
• Point 2: $(0, 6)$
• Point 3: $(2, 2)$

Step 4: Draw the line:

The line passes through these three points and represents the function $f(x) = -2x + 6$.

Would you like further assistance graphing this or exploring related concepts?

5 Related Questions:

1. How do you determine the slope of the function $f(x) = -2x + 6$?
2. What does the y-intercept of the function represent in this graph?
3. How would the graph change if the equation was $f(x) = 2x + 6$?
4. What are the x-intercepts and how are they found in this graph?
5. How would you extend the table to include more values of $x$?

Tip: When graphing, always verify your calculations and ensure the points align with the equation for accuracy.