Find the Domain and Range y=3csc(x)

$y = 3 \csc (x)$

Set the argument in $\csc (x)$ equal to $π n$ to find where the expression is undefined.

$x = π n$ , for any integer $n$

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

Set-Builder Notation:

${x | x \neq π n}$ , for any integer $n$

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

Interval Notation:

$(- \infty, - 3] \cup [3, \infty)$

Set-Builder Notation:

${y | y \leq - 3, y \geq 3}$

Determine the domain and range.

Domain: ${x | x \neq π n}$ , for any integer $n$

Range: $(- \infty, - 3] \cup [3, \infty), {y | y \leq - 3, y \geq 3}$