Graph Using a Table of Values f(x)=(x^2-4)/(x-2)

$f (x) = \frac{x^{2} - 4}{x - 2}$

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Simplify $\frac{{(- 2)}^{2} - 4}{(- 2) - 2}$ .

Simplify the numerator.

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

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

Subtract $4$ from $4$ .

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

Simplify the expression.

Subtract $2$ from $- 2$ .

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

Divide $0$ by $- 4$ .

$y = 0$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Simplify $\frac{{(- 1)}^{2} - 4}{(- 1) - 2}$ .

Simplify the numerator.

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

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

Subtract $4$ from $1$ .

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

Simplify the expression.

Subtract $2$ from $- 1$ .

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

Divide $- 3$ by $- 3$ .

$y = 1$

Step 5

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

$y = \frac{{(0)}^{2} - 4}{(0) - 2}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{0^{2} - 4}{(0) - 2}$

Remove parentheses.

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

Remove parentheses.

$y = \frac{{(0)}^{2} - 4}{(0) - 2}$

Simplify $\frac{{(0)}^{2} - 4}{(0) - 2}$ .

Simplify the numerator.

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

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

Subtract $4$ from $0$ .

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

Simplify the expression.

Subtract $2$ from $0$ .

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

Divide $- 4$ by $- 2$ .

$y = 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = \frac{1^{2} - 4}{1 - 2}$

Remove parentheses.

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

Simplify $\frac{{(1)}^{2} - 4}{(1) - 2}$ .

Simplify the numerator.

One to any power is one.

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

Subtract $4$ from $1$ .

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

Simplify the expression.

Subtract $2$ from $1$ .

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

Divide $- 3$ by $- 1$ .

$y = 3$

Step 9

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

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

Step 10

Graph Using a Table of Values f(x)=(x^2-4)/(x-2)

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