Graph Using a Table of Values f(x)=(-10x+20)/(x^2-3x-10)

$f (x) = \frac{- 10 x + 20}{x^{2} - 3 x - 10}$

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

$y = \frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - 3 \cdot - 1 - 10}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - 3 \cdot - 1 - 10}$

Simplify $\frac{- 10 \cdot - 1 + 20}{{(- 1)}^{2} - 3 \cdot - 1 - 10}$ .

Simplify the numerator.

Multiply $- 10$ by $- 1$ .

$y = \frac{10 + 20}{{(- 1)}^{2} - 3 \cdot - 1 - 10}$

Add $10$ and $20$ .

$y = \frac{30}{{(- 1)}^{2} - 3 \cdot - 1 - 10}$

Simplify the denominator.

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

$y = \frac{30}{1 - 3 \cdot - 1 - 10}$

Multiply $- 3$ by $- 1$ .

$y = \frac{30}{1 + 3 - 10}$

Add $1$ and $3$ .

$y = \frac{30}{4 - 10}$

Subtract $10$ from $4$ .

$y = \frac{30}{- 6}$

Divide $30$ by $- 6$ .

$y = - 5$

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

$y = \frac{- 10 \cdot 0 + 20}{{(0)}^{2} - 3 \cdot 0 - 10}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 0 + 20}{0^{2} - 3 \cdot 0 - 10}$

Remove parentheses.

$y = \frac{- 10 \cdot 0 + 20}{{(0)}^{2} - 3 \cdot 0 - 10}$

Simplify $\frac{- 10 \cdot 0 + 20}{{(0)}^{2} - 3 \cdot 0 - 10}$ .

Simplify the numerator.

Multiply $- 10$ by $0$ .

$y = \frac{0 + 20}{0^{2} - 3 \cdot 0 - 10}$

Add $0$ and $20$ .

$y = \frac{20}{0^{2} - 3 \cdot 0 - 10}$

Simplify the denominator.

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

$y = \frac{20}{0 - 3 \cdot 0 - 10}$

Multiply $- 3$ by $0$ .

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

Add $0$ and $0$ .

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

Subtract $10$ from $0$ .

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

Divide $20$ by $- 10$ .

$y = - 2$

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

$y = \frac{- 10 \cdot 1 + 20}{{(1)}^{2} - 3 \cdot 1 - 10}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 1 + 20}{1^{2} - 3 \cdot 1 - 10}$

Remove parentheses.

$y = \frac{- 10 \cdot 1 + 20}{{(1)}^{2} - 3 \cdot 1 - 10}$

Simplify $\frac{- 10 \cdot 1 + 20}{{(1)}^{2} - 3 \cdot 1 - 10}$ .

Simplify the numerator.

Multiply $- 10$ by $1$ .

$y = \frac{- 10 + 20}{1^{2} - 3 \cdot 1 - 10}$

Add $- 10$ and $20$ .

$y = \frac{10}{1^{2} - 3 \cdot 1 - 10}$

Simplify the denominator.

One to any power is one.

$y = \frac{10}{1 - 3 \cdot 1 - 10}$

Multiply $- 3$ by $1$ .

$y = \frac{10}{1 - 3 - 10}$

Subtract $3$ from $1$ .

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

Subtract $10$ from $- 2$ .

$y = \frac{10}{- 12}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $10$ and $- 12$ .

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 12}$

Cancel the common factors.

Factor $2$ out of $- 12$ .

$y = \frac{2 \cdot 5}{2 \cdot - 6}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 6}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$y = \frac{- 10 \cdot 2 + 20}{{(2)}^{2} - 3 \cdot 2 - 10}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{- 10 \cdot 2 + 20}{2^{2} - 3 \cdot 2 - 10}$

Remove parentheses.

$y = \frac{- 10 \cdot 2 + 20}{{(2)}^{2} - 3 \cdot 2 - 10}$

Simplify $\frac{- 10 \cdot 2 + 20}{{(2)}^{2} - 3 \cdot 2 - 10}$ .

Cancel the common factor of $- 10 \cdot 2 + 20$ and ${(2)}^{2} - 3 \cdot 2 - 10$ .

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

$y = \frac{2 (- 5 \cdot 2) + 20}{{(2)}^{2} - 3 \cdot 2 - 10}$

Factor $2$ out of $20$ .

$y = \frac{2 (- 5 \cdot 2) + 2 \cdot 10}{2^{2} - 3 \cdot 2 - 10}$

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

$y = \frac{2 (- 5 \cdot 2 + 10)}{{(2)}^{2} - 3 \cdot 2 - 10}$

Cancel the common factors.

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

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot 2 - 3 \cdot 2 - 10}$

Factor $2$ out of $- 3 \cdot 2$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot 2 + 2 \cdot - 3 - 10}$

Factor $2$ out of $2 \cdot 2 + 2 \cdot - 3$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 3) - 10}$

Factor $2$ out of $- 10$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 3) + 2 (- 5)}$

Factor $2$ out of $2 \cdot (2 - 3) + 2 (- 5)$ .

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 3 - 5)}$

Cancel the common factor.

$y = \frac{2 (- 5 \cdot 2 + 10)}{2 \cdot (2 - 3 - 5)}$

Rewrite the expression.

$y = \frac{- 5 \cdot 2 + 10}{2 - 3 - 5}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

$y = \frac{- 10 + 10}{2 - 3 - 5}$

Add $- 10$ and $10$ .

$y = \frac{0}{2 - 3 - 5}$

Simplify the denominator.

Subtract $3$ from $2$ .

$y = \frac{0}{- 1 - 5}$

Subtract $5$ from $- 1$ .

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

Divide $0$ by $- 6$ .

$y = 0$

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

$\begin{array}{c} x & y \\ - 1 & - 5 \\ 0 & - 2 \\ 1 & - \frac{5}{6} \\ 2 & 0 \end{array}$

Graph Using a Table of Values f(x)=(-10x+20)/(x^2-3x-10)

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