Precalculus Examples

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

Step 1

Set the denominator in $\frac{x - 3}{x + 2}$ equal to $0$ to find where the expression is undefined.

$x + 2 = 0$

Step 2

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 3

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$(- \infty, - 2) \cup (- 2, \infty)$

Set-Builder Notation:

${x | x \neq - 2}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, 1) \cup (1, \infty)$

Set-Builder Notation:

${y | y \neq 1}$

Step 5

Determine the domain and range.

Domain: $(- \infty, - 2) \cup (- 2, \infty), {x | x \neq - 2}$

Range: $(- \infty, 1) \cup (1, \infty), {y | y \neq 1}$

Step 6