Graph Using a Table of Values f(x)=(-6x-12)/(x^2+x-12)

$f (x) = \frac{- 6 x - 12}{x^{2} + x - 12}$

Step 1

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

$y = \frac{- 6 \cdot - 2 - 12}{{(- 2)}^{2} - 2 - 12}$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 6 \cdot - 2 - 12}{{(- 2)}^{2} - 2 - 12}$

Simplify $\frac{- 6 \cdot - 2 - 12}{{(- 2)}^{2} - 2 - 12}$ .

Simplify the numerator.

Multiply $- 6$ by $- 2$ .

$y = \frac{12 - 12}{{(- 2)}^{2} - 2 - 12}$

Subtract $12$ from $12$ .

$y = \frac{0}{{(- 2)}^{2} - 2 - 12}$

Simplify the denominator.

Raise $- 2$ to the power of $2$ .

$y = \frac{0}{4 - 2 - 12}$

Subtract $2$ from $4$ .

$y = \frac{0}{2 - 12}$

Subtract $12$ from $2$ .

$y = \frac{0}{- 10}$

Divide $0$ by $- 10$ .

$y = 0$

Step 3

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

$y = \frac{- 6 \cdot - 1 - 12}{{(- 1)}^{2} - 1 - 12}$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 6 \cdot - 1 - 12}{{(- 1)}^{2} - 1 - 12}$

Simplify $\frac{- 6 \cdot - 1 - 12}{{(- 1)}^{2} - 1 - 12}$ .

Simplify the numerator.

Multiply $- 6$ by $- 1$ .

$y = \frac{6 - 12}{{(- 1)}^{2} - 1 - 12}$

Subtract $12$ from $6$ .

$y = \frac{- 6}{{(- 1)}^{2} - 1 - 12}$

Simplify the denominator.

Raise $- 1$ to the power of $2$ .

$y = \frac{- 6}{1 - 1 - 12}$

Subtract $1$ from $1$ .

$y = \frac{- 6}{0 - 12}$

Subtract $12$ from $0$ .

$y = \frac{- 6}{- 12}$

Cancel the common factor of $- 6$ and $- 12$ .

Factor $- 6$ out of $- 6$ .

$y = \frac{- 6 (1)}{- 12}$

Cancel the common factors.

Factor $- 6$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

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

$y = \frac{- 6 \cdot 0 - 12}{{(0)}^{2} + 0 - 12}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 6 \cdot 0 - 12}{{(0)}^{2} + 0 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 0 - 12}{0^{2} + 0 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 0 - 12}{{(0)}^{2} + 0 - 12}$

Simplify $\frac{- 6 \cdot 0 - 12}{{(0)}^{2} + 0 - 12}$ .

Simplify the numerator.

Multiply $- 6$ by $0$ .

$y = \frac{0 - 12}{0^{2} + 0 - 12}$

Subtract $12$ from $0$ .

$y = \frac{- 12}{0^{2} + 0 - 12}$

Simplify the denominator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{- 12}{0 + 0 - 12}$

Add $0$ and $0$ .

$y = \frac{- 12}{0 - 12}$

Subtract $12$ from $0$ .

$y = \frac{- 12}{- 12}$

Divide $- 12$ by $- 12$ .

$y = 1$

Step 7

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

$y = \frac{- 6 \cdot 1 - 12}{{(1)}^{2} + 1 - 12}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 6 \cdot 1 - 12}{{(1)}^{2} + 1 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 1 - 12}{1^{2} + 1 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 1 - 12}{{(1)}^{2} + 1 - 12}$

Simplify $\frac{- 6 \cdot 1 - 12}{{(1)}^{2} + 1 - 12}$ .

Simplify the numerator.

Multiply $- 6$ by $1$ .

$y = \frac{- 6 - 12}{1^{2} + 1 - 12}$

Subtract $12$ from $- 6$ .

$y = \frac{- 18}{1^{2} + 1 - 12}$

Simplify the denominator.

One to any power is one.

$y = \frac{- 18}{1 + 1 - 12}$

Add $1$ and $1$ .

$y = \frac{- 18}{2 - 12}$

Subtract $12$ from $2$ .

$y = \frac{- 18}{- 10}$

Cancel the common factor of $- 18$ and $- 10$ .

Factor $- 2$ out of $- 18$ .

$y = \frac{- 2 (9)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$y = \frac{- 2 \cdot 9}{- 2 \cdot 5}$

Cancel the common factor.

$y = \frac{- 2 \cdot 9}{- 2 \cdot 5}$

Rewrite the expression.

$y = \frac{9}{5}$

Step 9

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

$y = \frac{- 6 \cdot 2 - 12}{{(2)}^{2} + 2 - 12}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 6 \cdot 2 - 12}{{(2)}^{2} + 2 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 2 - 12}{2^{2} + 2 - 12}$

Remove parentheses.

$y = \frac{- 6 \cdot 2 - 12}{{(2)}^{2} + 2 - 12}$

Simplify $\frac{- 6 \cdot 2 - 12}{{(2)}^{2} + 2 - 12}$ .

Cancel the common factor of $- 6 \cdot 2 - 12$ and ${(2)}^{2} + 2 - 12$ .

Factor $2$ out of $- 6 \cdot 2$ .

$y = \frac{2 (- 3 \cdot 2) - 12}{{(2)}^{2} + 2 - 12}$

Factor $2$ out of $- 12$ .

$y = \frac{2 (- 3 \cdot 2) + 2 \cdot - 6}{2^{2} + 2 - 12}$

Factor $2$ out of $2 (- 3 \cdot 2) + 2 (- 6)$ .

$y = \frac{2 (- 3 \cdot 2 - 6)}{{(2)}^{2} + 2 - 12}$

Cancel the common factors.

Factor $2$ out of ${(2)}^{2}$ .

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot 2 + 2 - 12}$

Factor $2$ out of $2$ .

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot 2 + 2 (1) - 12}$

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

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot (2 + 1) - 12}$

Factor $2$ out of $- 12$ .

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot (2 + 1) + 2 (- 6)}$

Factor $2$ out of $2 \cdot (2 + 1) + 2 (- 6)$ .

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot (2 + 1 - 6)}$

Cancel the common factor.

$y = \frac{2 (- 3 \cdot 2 - 6)}{2 \cdot (2 + 1 - 6)}$

Rewrite the expression.

$y = \frac{- 3 \cdot 2 - 6}{2 + 1 - 6}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

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

Subtract $6$ from $- 6$ .

$y = \frac{- 12}{2 + 1 - 6}$

Simplify the denominator.

Add $2$ and $1$ .

$y = \frac{- 12}{3 - 6}$

Subtract $6$ from $3$ .

$y = \frac{- 12}{- 3}$

Divide $- 12$ by $- 3$ .

$y = 4$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & \frac{1}{2} \\ 0 & 1 \\ 1 & \frac{9}{5} \\ 2 & 4 \end{array}$

Step 12

Graph Using a Table of Values f(x)=(-6x-12)/(x^2+x-12)

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