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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $0$ .

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

Simplify the denominator.

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

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

Multiply $3$ by $0$ .

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

Add $0$ and $0$ .

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

Add $0$ and $2$ .

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

Divide $- 2$ by $2$ .

$y = - 1$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $1$ .

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

Simplify the denominator.

One to any power is one.

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

Multiply $3$ by $1$ .

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

Add $1$ and $3$ .

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

Add $4$ and $2$ .

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

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Reduce the expression by cancelling the common factors.

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $- 2$ .

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

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

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

Cancel the common factors.

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

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

Factor $2$ out of $3 (2)$ .

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

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

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

Factor $2$ out of $2$ .

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

Factor $2$ out of $2 \cdot (2 + 3) + 2 (1)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $1$ from $1$ .

$y = \frac{0}{2 + 3 + 1}$

Simplify the denominator.

Add $2$ and $3$ .

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

Add $5$ and $1$ .

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

Divide $0$ by $6$ .

$y = 0$

Step 7

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

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

Step 8

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

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