Algebra Examples

y = sec (x)

$y = \sec (x)$

Step 1

Set the argument in

sec (x)

$\sec (x)$ equal to

\frac{π}{2} + π n

$\frac{π}{2} + π n$ to find where the expression is undefined.

x = \frac{π}{2} + π n

$x = \frac{π}{2} + π n$ , for any integer

n

$n$

Step 2

The domain is all values of

x

$x$ that make the expression defined.

Set-Builder Notation:

{x ∣ ∣ x \neq \frac{π}{2} + π n}

${x | x \neq \frac{π}{2} + π n}$ , for any integer

n

$n$

Step 3

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

(- \infty, - 1] \cup [1, \infty)

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

Set-Builder Notation:

{y | y \leq - 1, y \geq 1}

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

Step 4

Determine the domain and range.

Domain:

{x ∣ ∣ x \neq \frac{π}{2} + π n}

${x | x \neq \frac{π}{2} + π n}$ , for any integer

n

$n$

Range:

(- \infty, - 1] \cup [1, \infty), {y | y \leq - 1, y \geq 1}

$(- \infty, - 1] \cup [1, \infty), {y | y \leq - 1, y \geq 1}$

Step 5