Complete the table and then graph the function.

f

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2

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f

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4

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3

4

Let's start by completing the table for the given function.

The function is: 

\[
f(x) = -2x
\]

We will substitute the values of \(x\) given in the table to find the corresponding values of \(f(x)\).

### Table Completion:

| \( x \) | \( f(x) = -2x \) |
|--------|------------------|
| -4     | \(-2(-4) = 8\)   |
| -3     | \(-2(-3) = 6\)   |
| -2     | \(-2(-2) = 4\)   |
|  3     | \(-2(3) = -6\)   |
|  4     | \(-2(4) = -8\)   |

So, the completed table looks like:

\[
\begin{array}{c|c}
x & f(x) = -2x \\
\hline
-4 & 8 \\
-3 & 6 \\
-2 & 4 \\
3  & -6 \\
4  & -8 \\
\end{array}
\]

### Graphing the function:

Now, to graph the function \( f(x) = -2x \), plot the points from the table and draw a straight line passing through them since this is a linear function.

1. Plot the points \((-4, 8)\), \((-3, 6)\), \((-2, 4)\), \((3, -6)\), \((4, -8)\) on a coordinate plane.
2. Draw a straight line through these points because the function is linear with a slope of -2 (the coefficient of \(x\)).

Would you like me to generate a graph for you?

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**Relative questions:**
1. What is the slope of the line represented by \( f(x) = -2x \)?
2. How does the graph of \( f(x) = -2x \) compare to \( f(x) = x \)?
3. What is the y-intercept of the function \( f(x) = -2x \)?
4. How would the graph change if the function were \( f(x) = 2x \)?
5. Can you explain how negative slopes affect the direction of the line?

**Tip:** For linear functions, the slope determines how steep the line is and whether it slants upwards (positive slope) or downwards (negative slope).

Complete the table and then graph the function. f(x) = -2x

Learn how to complete a table and graph the linear function f(x) = -2x. This problem involves key algebraic concepts, including linear functions and graphing points on a coordinate plane. Suitable for students in Grades 6-8.

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