Graph Using a Table of Values f(x)=(-10x+20)/(x^2-x-20)

$f (x) = \frac{- 10 x + 20}{x^{2} - x - 20}$

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

$y = \frac{- 10 \cdot - 2 + 20}{{(- 2)}^{2} - (- 2) - 20}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot - 2 + 20}{{(- 2)}^{2} - (- 2) - 20}$

Simplify $\frac{- 10 \cdot - 2 + 20}{{(- 2)}^{2} - (- 2) - 20}$ .

Simplify the numerator.

Multiply $- 10$ by $- 2$ .

$y = \frac{20 + 20}{{(- 2)}^{2} - (- 2) - 20}$

Add $20$ and $20$ .

$y = \frac{40}{{(- 2)}^{2} - (- 2) - 20}$

Simplify the denominator.

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

$y = \frac{40}{4 - (- 2) - 20}$

Multiply $- 1$ by $- 2$ .

$y = \frac{40}{4 + 2 - 20}$

Add $4$ and $2$ .

$y = \frac{40}{6 - 20}$

Subtract $20$ from $6$ .

$y = \frac{40}{- 14}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $40$ and $- 14$ .

Factor $2$ out of $40$ .

$y = \frac{2 (20)}{- 14}$

Cancel the common factors.

Factor $2$ out of $- 14$ .

$y = \frac{2 \cdot 20}{2 \cdot - 7}$

Cancel the common factor.

$y = \frac{2 \cdot 20}{2 \cdot - 7}$

Rewrite the expression.

$y = \frac{20}{- 7}$

Move the negative in front of the fraction.

$y = - \frac{20}{7}$

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

$y = \frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - (- 1) - 20}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - (- 1) - 20}$

Simplify $\frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - (- 1) - 20}$ .

Simplify the numerator.

Multiply $- 10$ by $- 1$ .

$y = \frac{10 + 20}{{(- 1)}^{2} - (- 1) - 20}$

Add $10$ and $20$ .

$y = \frac{30}{{(- 1)}^{2} - (- 1) - 20}$

Simplify the denominator.

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

$y = \frac{30}{1 - (- 1) - 20}$

Multiply $- 1$ by $- 1$ .

$y = \frac{30}{1 + 1 - 20}$

Add $1$ and $1$ .

$y = \frac{30}{2 - 20}$

Subtract $20$ from $2$ .

$y = \frac{30}{- 18}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $30$ and $- 18$ .

Factor $6$ out of $30$ .

$y = \frac{6 (5)}{- 18}$

Cancel the common factors.

Factor $6$ out of $- 18$ .

$y = \frac{6 \cdot 5}{6 \cdot - 3}$

Cancel the common factor.

$y = \frac{6 \cdot 5}{6 \cdot - 3}$

Rewrite the expression.

$y = \frac{5}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{5}{3}$

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

$y = \frac{- 10 \cdot 0 + 20}{{(0)}^{2} - (0) - 20}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 0 + 20}{0^{2} - (0) - 20}$

Remove parentheses.

$y = \frac{- 10 \cdot 0 + 20}{{(0)}^{2} - (0) - 20}$

Simplify $\frac{- 10 \cdot 0 + 20}{{(0)}^{2} - (0) - 20}$ .

Simplify the numerator.

Multiply $- 10$ by $0$ .

$y = \frac{0 + 20}{0^{2} - (0) - 20}$

Add $0$ and $20$ .

$y = \frac{20}{0^{2} - (0) - 20}$

Simplify the denominator.

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

$y = \frac{20}{0 - (0) - 20}$

Multiply $- 1$ by $0$ .

$y = \frac{20}{0 + 0 - 20}$

Add $0$ and $0$ .

$y = \frac{20}{0 - 20}$

Subtract $20$ from $0$ .

$y = \frac{20}{- 20}$

Divide $20$ by $- 20$ .

$y = - 1$

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

$y = \frac{- 10 \cdot 1 + 20}{{(1)}^{2} - (1) - 20}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 1 + 20}{1^{2} - (1) - 20}$

Remove parentheses.

$y = \frac{- 10 \cdot 1 + 20}{{(1)}^{2} - (1) - 20}$

Simplify $\frac{- 10 \cdot 1 + 20}{{(1)}^{2} - (1) - 20}$ .

Simplify the numerator.

Multiply $- 10$ by $1$ .

$y = \frac{- 10 + 20}{1^{2} - (1) - 20}$

Add $- 10$ and $20$ .

$y = \frac{10}{1^{2} - (1) - 20}$

Simplify the denominator.

One to any power is one.

$y = \frac{10}{1 - (1) - 20}$

Multiply $- 1$ by $1$ .

$y = \frac{10}{1 - 1 - 20}$

Subtract $1$ from $1$ .

$y = \frac{10}{0 - 20}$

Subtract $20$ from $0$ .

$y = \frac{10}{- 20}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $- 20$ .

Factor $10$ out of $10$ .

$y = \frac{10 (1)}{- 20}$

Cancel the common factors.

Factor $10$ out of $- 20$ .

$y = \frac{10 \cdot 1}{10 \cdot - 2}$

Cancel the common factor.

$y = \frac{10 \cdot 1}{10 \cdot - 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$y = \frac{- 10 \cdot 2 + 20}{{(2)}^{2} - (2) - 20}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 2 + 20}{2^{2} - (2) - 20}$

Remove parentheses.

$y = \frac{- 10 \cdot 2 + 20}{{(2)}^{2} - (2) - 20}$

Simplify $\frac{- 10 \cdot 2 + 20}{{(2)}^{2} - (2) - 20}$ .

Cancel the common factor of $- 10 \cdot 2 + 20$ and ${(2)}^{2} - (2) - 20$ .

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

$y = \frac{2 (- 5 \cdot 2) + 20}{{(2)}^{2} - (2) - 20}$

Factor $2$ out of $20$ .

$y = \frac{2 (- 5 \cdot 2) + 2 \cdot 10}{2^{2} - (2) - 20}$

Factor $2$ out of $2 (- 5 \cdot 2) + 2 (10)$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{{(2)}^{2} - (2) - 20}$

Cancel the common factors.

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

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot 2 - (2) - 20}$

Factor $2$ out of $- (2)$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot 2 + 2 \cdot - 1 - 20}$

Factor $2$ out of $2 \cdot 2 + 2 \cdot - 1$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 1) - 20}$

Factor $2$ out of $- 20$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 1) + 2 (- 10)}$

Factor $2$ out of $2 \cdot (2 - 1) + 2 (- 10)$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 1 - 10)}$

Cancel the common factor.

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 1 - 10)}$

Rewrite the expression.

$y = \frac{- 5 \cdot 2 + 10}{2 - 1 - 10}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

$y = \frac{- 10 + 10}{2 - 1 - 10}$

Add $- 10$ and $10$ .

$y = \frac{0}{2 - 1 - 10}$

Simplify the denominator.

Subtract $1$ from $2$ .

$y = \frac{0}{1 - 10}$

Subtract $10$ from $1$ .

$y = \frac{0}{- 9}$

Divide $0$ by $- 9$ .

$y = 0$

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

$\begin{array}{c} x & y \\ - 2 & - \frac{20}{7} \\ - 1 & - \frac{5}{3} \\ 0 & - 1 \\ 1 & - \frac{1}{2} \\ 2 & 0 \end{array}$

Graph Using a Table of Values f(x)=(-10x+20)/(x^2-x-20)

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