Math Problem Statement

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

F(x) = 

x + 2

xF(x)

−2   −1   2   7   14   23  

Solution

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

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

Table completion:

We compute F(x)F(x) for the values of x=2,1,2,7,14,23x = -2, -1, 2, 7, 14, 23.

F(x)=x+2F(x) = x + 2

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

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

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

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

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

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

Completed table:

\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)$$ on the graph, then draw a straight line through them. --- Do you want a graph generated for this, or do you have any questions on how to plot it? --- Here are 5 relative questions: 1. How do you find the slope of a linear function? 2. What is the significance of the y-intercept in a function? 3. How would you graph a non-linear function, like a quadratic? 4. What happens to the graph of $$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.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

F(x) = x + 2

Theorems

Linear Equation Theorem

Suitable Grade Level

Grades 6-8