Chapter 3.1, Problem 39E

To determine

Draw the graph and also construct a value table of the given function $f(x)=6^x$ by using graphing utility, and also find any asymptotes of the graph.

Explanation of Solution

Given information:

It is given in the question that the given exponential function is $f(x)=6^x$ .

Graph:

Interpretation:

By putting the values of x in the given function we get the value of y and then plot it and make the graph of the given function $f(x)=6^x$ .

By putting $x=-2$ ,

  $\begin{array}{l}$ f(-2)={(6)}^{-2}$={\left(\frac{1}{6}\right)}^2\\ =\left(\frac{1}{36}\right)\\ =0.027\end{array}$

By putting $x=-1$ ,

  $\begin{array}{l}$ f(-1)={(6)}^{-1}$={\left(\frac{1}{6}\right)}^1\\ =0.166\end{array}$

By putting $x=0$ ,

  $\begin{array}{l}$ f(0)={(6)}^0$=1\end{array}$

By putting $x=1$ ,

  $\begin{array}{l}$ f(1)={(6)}^1$=6\end{array}$

By putting $x=2$ ,

  $\begin{array}{l}$ f(2)={(6)}^2$=36\end{array}$

So the table is,

$x$	$f(x)=6^x$
-2	0.027
-1	0.166
0	1
1	6
2	36

And asymptotes is $y=0$ .