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

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

Step 1

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

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

Step 2

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

Simplify the numerator.

Multiply $3$ by $- 2$ .

$y = \frac{- 6 - 3}{- (- 2) + 2}$

Subtract $3$ from $- 6$ .

$y = \frac{- 9}{- (- 2) + 2}$

Simplify the denominator.

Multiply $- 1$ by $- 2$ .

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

Add $2$ and $2$ .

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

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

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

Simplify the numerator.

Multiply $3$ by $- 1$ .

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

Subtract $3$ from $- 3$ .

$y = \frac{- 6}{- (- 1) + 2}$

Simplify the denominator.

Multiply $- 1$ by $- 1$ .

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

Add $1$ and $2$ .

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

Divide $- 6$ by $3$ .

$y = - 2$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the numerator.

Multiply $3$ by $0$ .

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

Subtract $3$ from $0$ .

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

Simplify the denominator.

Multiply $- 1$ by $0$ .

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

Add $0$ and $2$ .

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

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the numerator.

Multiply $3$ by $1$ .

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

Subtract $3$ from $3$ .

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

Simplify the denominator.

Multiply $- 1$ by $1$ .

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

Add $- 1$ and $2$ .

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

Divide $0$ by $1$ .

$y = 0$

Step 9

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

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

Step 10

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

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