Chapter A, Problem 1E

To determine

To graph: The equation, $y=3^x$.

Explanation of Solution

Given Information:

The provided equation is $y=3^x$.

Graph:

Consider the equation, $y=3^x$.

To draw the graph of $y=3^x$, first compute the value of y for different values of x.

Compute the value of y at $x=1$ by substituting $x=1$ in the equation $y=3^x$ as,

$\begin{array}{c}y\left(1\right)=3^1\\ =3\end{array}$

Compute the value of y at $x=0$ by substituting $x=0$ in the equation $y=3^x$ as,

$\begin{array}{c}y\left(0\right)=3^0\\ =1\end{array}$

Compute the value of y at $x=3$ by substituting $x=3$ in the equation $y=3^x$ as,

$\begin{array}{c}y\left(3\right)=3^3\\ =27\end{array}$

Compute the value of y at $x=-1$ by substituting $x=-1$ in the equation $y=3^x$ as,

$\begin{array}{c}y\left(-1\right)=3^{-1}\\ =0.333\end{array}$

Thus, the ordered pairs formed are,

x	y
$1$	$3$
$0$	$1$
$3$	$27$
$-1$	$0.333$

Now plot the graph of the equation $y=3^x$ as follows:

Step $1$: Mark the points $\left(1,3\right)$, $\left(0,1\right)$, $\left(3,27\right)$ and $\left(-1,0.333\right)$ on the graph.

Step $2$: Join the points.

The graph obtained as,

Interpretation:

It is interpreted from the above graph that the equation $y=3^x$ is an increasing exponential function as the value of y increases with the increase in x.