Precalculus Examples

$f (x) = \arctan (x)$

Step 1

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

Interval Notation:

$(- \frac{π}{2}, \frac{π}{2})$

Set-Builder Notation:

${y | - \frac{π}{2} < y < \frac{π}{2}}$

Step 2

There are two horizontal asymptotes.

Horizontal Asymptotes: $y = - \frac{π}{2}$ , $y = \frac{π}{2}$

No Vertical Asymptotes

No Oblique Asymptotes

Step 3