Precalculus Examples

$h (x) = \ln (x + 5)$

Step 1

Set the argument in $\ln (x + 5)$ greater than $0$ to find where the expression is defined.

$x + 5 > 0$

Step 2

Subtract $5$ from both sides of the inequality.

$x > - 5$

Step 3

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

Interval Notation:

$(- 5, \infty)$

Set-Builder Notation:

${x | x > - 5}$

Step 4

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

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(- 5, \infty), {x | x > - 5}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6