Trigonometry Examples

F (x) = 2 cos (x - 3)

$F (x) = 2 \cos (x - 3)$

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)

$(- \infty, \infty)$

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:

$[- 2, 2]$

Set-Builder Notation:

${y | - 2 \leq y \leq 2}$

Step 3

Determine the domain and range.

Domain:

$(- \infty, \infty), {x | x \in ℝ}$

Range:

$[- 2, 2], {y | - 2 \leq y \leq 2}$

Step 4