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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $2$ by $- 2$ .

$y = \frac{- 4 + 3}{- 2 + 3}$

Add $- 4$ and $3$ .

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

Simplify the expression.

Add $- 2$ and $3$ .

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

Divide $- 1$ by $1$ .

$y = - 1$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $2$ by $- 1$ .

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

Add $- 2$ and $3$ .

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

Add $- 1$ and $3$ .

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Cancel the common factor of $2 (0) + 3$ and $(0) + 3$ .

Factor $3$ out of $2 (0)$ .

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

Factor $3$ out of $3$ .

$y = \frac{3 (2 \cdot (0)) + 3 (1)}{(0) + 3}$

Factor $3$ out of $3 (2 \cdot (0)) + 3 (1)$ .

$y = \frac{3 (2 \cdot (0) + 1)}{(0) + 3}$

Cancel the common factors.

Factor $3$ out of $0$ .

$y = \frac{3 (2 \cdot (0) + 1)}{3 (0) + 3}$

Factor $3$ out of $3$ .

$y = \frac{3 (2 \cdot (0) + 1)}{3 \cdot 0 + 3 \cdot 1}$

Factor $3$ out of $3 \cdot 0 + 3 \cdot 1$ .

$y = \frac{3 (2 \cdot (0) + 1)}{3 \cdot (0 + 1)}$

Cancel the common factor.

$y = \frac{3 (2 \cdot (0) + 1)}{3 \cdot (0 + 1)}$

Rewrite the expression.

$y = \frac{2 \cdot (0) + 1}{0 + 1}$

Simplify the numerator.

Multiply $2$ by $0$ .

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

Add $0$ and $1$ .

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

Simplify the expression.

Add $0$ and $1$ .

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

Divide $1$ by $1$ .

$y = 1$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $2$ by $1$ .

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

Add $2$ and $3$ .

$y = \frac{5}{1 + 3}$

Add $1$ and $3$ .

$y = \frac{5}{4}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the numerator.

Multiply $2$ by $2$ .

$y = \frac{4 + 3}{2 + 3}$

Add $4$ and $3$ .

$y = \frac{7}{2 + 3}$

Add $2$ and $3$ .

$y = \frac{7}{5}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 1 \\ - 1 & \frac{1}{2} \\ 0 & 1 \\ 1 & \frac{5}{4} \\ 2 & \frac{7}{5} \end{array}$

Step 12

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

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