Graph Using a Table of Values f(x)=(3x+3)/(x+2)

$f (x) = \frac{3 x + 3}{x + 2}$

Step 1

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{3 (- 1) + 3}{(- 1) + 2}$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{3 (- 1) + 3}{- 1 + 2}$

Remove parentheses.

$y = \frac{3 (- 1) + 3}{(- 1) + 2}$

Simplify $\frac{3 (- 1) + 3}{(- 1) + 2}$ .

Simplify the numerator.

Multiply $3$ by $- 1$ .

$y = \frac{- 3 + 3}{- 1 + 2}$

Add $- 3$ and $3$ .

$y = \frac{0}{- 1 + 2}$

Simplify the expression.

Add $- 1$ and $2$ .

$y = \frac{0}{1}$

Divide $0$ by $1$ .

$y = 0$

Step 3

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{3 (0) + 3}{(0) + 2}$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{3 (0) + 3}{0 + 2}$

Remove parentheses.

$y = \frac{3 (0) + 3}{(0) + 2}$

Simplify $\frac{3 (0) + 3}{(0) + 2}$ .

Simplify the numerator.

Multiply $3$ by $0$ .

$y = \frac{0 + 3}{0 + 2}$

Add $0$ and $3$ .

$y = \frac{3}{0 + 2}$

Add $0$ and $2$ .

$y = \frac{3}{2}$

Step 5

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{3 (1) + 3}{(1) + 2}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{3 (1) + 3}{1 + 2}$

Remove parentheses.

$y = \frac{3 (1) + 3}{(1) + 2}$

Simplify $\frac{3 (1) + 3}{(1) + 2}$ .

Simplify the numerator.

Multiply $3$ by $1$ .

$y = \frac{3 + 3}{1 + 2}$

Add $3$ and $3$ .

$y = \frac{6}{1 + 2}$

Simplify the expression.

Add $1$ and $2$ .

$y = \frac{6}{3}$

Divide $6$ by $3$ .

$y = 2$

Step 7

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{3 (2) + 3}{(2) + 2}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{3 (2) + 3}{2 + 2}$

Remove parentheses.

$y = \frac{3 (2) + 3}{(2) + 2}$

Simplify $\frac{3 (2) + 3}{(2) + 2}$ .

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{6 + 3}{2 + 2}$

Add $6$ and $3$ .

$y = \frac{9}{2 + 2}$

Add $2$ and $2$ .

$y = \frac{9}{4}$

Step 9

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 1 & 0 \\ 0 & \frac{3}{2} \\ 1 & 2 \\ 2 & \frac{9}{4} \end{array}$

Step 10

Graph Using a Table of Values f(x)=(3x+3)/(x+2)

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