Chapter 11.2, Problem 8GCE

To determine

To explain the existence or absence of the asymptotes in exponential function.

Explanation of Solution

Given:

The given function is $y=a^x$

Calculation:

There is only presence of horizontal asymptote.

The following is the graph of the function $y=a^x$

  

The graphs has horizontal asymptote because the curve will always approach the x axis either in positive or negative direction but will never cross the x-axis and will never be equal to zero.

Clearly for positive values of $a$ the graph is increasing and for negative values of $a$ the graph is decreasing.