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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the expression.

Multiply $2$ by $- 2$ .

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

Subtract $3$ from $- 2$ .

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

Dividing two negative values results in a positive value.

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

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Simplify the expression.

Multiply $2$ by $- 1$ .

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

Subtract $3$ from $- 1$ .

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

Cancel the common factor of $- 2$ and $- 4$ .

Factor $- 2$ out of $- 2$ .

$y = \frac{- 2 (1)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

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

Cancel the common factors.

Factor $3$ out of $0$ .

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

Factor $3$ out of $- 3$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $0$ .

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

Simplify the expression.

Subtract $1$ from $0$ .

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

Divide $0$ by $- 1$ .

$y = 0$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Multiply $2$ by $1$ .

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

Subtract $3$ from $1$ .

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

Divide $2$ by $- 2$ .

$y = - 1$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

Multiply $2$ by $2$ .

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

Subtract $3$ from $2$ .

$y = \frac{4}{- 1}$

Divide $4$ by $- 1$ .

$y = - 4$

Step 11

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

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

Step 12

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

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