Find Three Ordered Pair Solutions f(x)=(-x-3)/(x+2)

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

Step 1

Write $f (x) = \frac{- x - 3}{x + 2}$ as an equation.

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

Step 2

Simplify $\frac{- x - 3}{x + 2}$ .

Factor $- 1$ out of $- x$ .

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

Rewrite $- 3$ as $- 1 (3)$ .

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

Factor $- 1$ out of $- (x) - 1 (3)$ .

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

Simplify the expression.

Rewrite $- (x + 3)$ as $- 1 (x + 3)$ .

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

Move the negative in front of the fraction.

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

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $3$ .

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

Add $0$ and $2$ .

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

Use the $x$ and $y$ values to form the ordered pair.

$(0, - \frac{3}{2})$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $1$ and $3$ .

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

Add $1$ and $2$ .

$y = - \frac{4}{3}$

Use the $x$ and $y$ values to form the ordered pair.

$(1, - \frac{4}{3})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $2$ and $3$ .

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

Add $2$ and $2$ .

$y = - \frac{5}{4}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, - \frac{5}{4})$

Step 7

These are three possible solutions to the equation.

$(0, - \frac{3}{2}), (1, - \frac{4}{3}), (2, - \frac{5}{4})$

Step 8

Find Three Ordered Pair Solutions f(x)=(-x-3)/(x+2)

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