Precalculus Examples

$f (x) = \frac{1 + e^{x} \sin (x)}{e^{x - 1} - 1}$

Step 1

Sine and cosine functions do not have asymptotes.

No Asymptotes

Step 2

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

Interval Notation:

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

Set-Builder Notation:

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

Step 3

The asymptote for $y = \frac{1 + e^{x} \sin (x)}{e^{x - 1} - 1}$ is $y = - 1, 1$ .

$y = - 1, 1$

Step 4