A function is given. Complete the table and then graph the function.

*F*(*x*) = 

*x* + 2

*xF*(*x*)

−2
 
−1
 
2
 
7
 
14
 
23
 

The given function is \( F(x) = x + 2 \).

Let's complete the table by calculating \( F(x) \) for each given \( x \) value.

### Table completion:
We compute \( F(x) \) for the values of \( x = -2, -1, 2, 7, 14, 23 \).

\[
F(x) = x + 2
\]

1. For \( x = -2 \):
\[
F(-2) = -2 + 2 = 0
\]

2. For \( x = -1 \):
\[
F(-1) = -1 + 2 = 1
\]

3. For \( x = 2 \):
\[
F(2) = 2 + 2 = 4
\]

4. For \( x = 7 \):
\[
F(7) = 7 + 2 = 9
\]

5. For \( x = 14 \):
\[
F(14) = 14 + 2 = 16
\]

6. For \( x = 23 \):
\[
F(23) = 23 + 2 = 25
\]

### Completed table:
\[
\begin{array}{|c|c|}
\hline
x & F(x) \\
\hline
-2 & 0 \\
-1 & 1 \\
2  & 4 \\
7  & 9 \\
14 & 16 \\
23 & 25 \\
\hline
\end{array}
\]

### Graphing the function:
This is a linear function, \( F(x) = x + 2 \), with a slope of 1 and a y-intercept of 2. Plot the points \((-2, 0)\), \((-1, 1)\), \((2, 4)\), \((7, 9)\), \((14, 16)\), and \((23, 25)\) on the graph, then draw a straight line through them.

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Do you want a graph generated for this, or do you have any questions on how to plot it?

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Here are 5 relative questions:
1. How do you find the slope of a linear function?
2. What is the significance of the y-intercept in a function?
3. How would you graph a non-linear function, like a quadratic?
4. What happens to the graph of \( F(x) \) if we add or subtract from the equation?
5. How can you determine if a function is increasing or decreasing?

**Tip:** Linear functions are always represented by straight lines, and their slope tells us the steepness or direction of the line.

A function is given. Complete the table and then graph the function.

F(x) = x + 2

xF(x)
−2
−1
2
7
14
23

Learn how to complete the table and graph the linear function F(x) = x + 2. This example covers fundamental algebraic concepts and is suitable for students in Grades 6-8. Includes a step-by-step table completion and instructions for graphing.

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