Chapter 3.1, Problem 9E

To determine

Draw the graph of the function $g(x)=5^x$ . Find the asymptotes, intercepts and also find, whether the graph is increasing or decreasing.

Explanation of Solution

Given information:

It is given in the question that, the exponential Function $g(x)=5^x$ .

  Graph:

Interpretation: The asymptotes of the function is $y=0$ .

The intercepts are:

  $y-$ intercepts = $(1,0)$

  $x-$ intercepts = none

And, by increasing the value of x in the given function y also increases.

For example:

By putting $x=2,3$ in the function $g(x)=5^x$

We get,

  $g(x)=25,125$ respectively.

So, the given function $g(x)=5^x$ is increasing function