Algebra Examples

$y = \cos (\frac{x}{2})$

Step 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 2

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

Interval Notation:

$[- 1, 1]$

Set-Builder Notation:

${y | - 1 \leq y \leq 1}$

Step 3

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $[- 1, 1], {y | - 1 \leq y \leq 1}$

Step 4