Chapter 3.1, Problem 14E

To determine

Draw the graph of the function $g(x)={\left(\frac{3}{2}\right)}^x$ . 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 $g(x)={\left(\frac{3}{2}\right)}^x$ .

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 $x=1,2$ in the function $g(x)={\left(\frac{3}{2}\right)}^x$

We get,

  $g(x)=\frac{3}{2}(=1.5)and\frac{9}{4}(=2.25)$ respectively.

So, the given function $g(x)={\left(\frac{3}{2}\right)}^x$ is increasing function.