91Ó°ÊÓ

The given equation is

$r=3^{\mathrm{θ}}$

Substitute $-\mathrm{θ}$for $\mathrm{θ}$in the equation

$$\begin{gathered} r=3^{-\mathrm{θ}} \\ r=\frac{1}{3^{\mathrm{θ}}} \end{gathered}$$

The equation does not match with the original equation so the test fails

the graph may or may not be symmetric with respect to the polar axis

Substitute $\mathrm{π}-\mathrm{θ}$for $\mathrm{θ}$in the equation

role="math" localid="1646691976744" $$\begin{gathered} r=3^{\mathrm{π}-\mathrm{θ}} \\ r=\frac{3^{\mathrm{π}}}{3^{\mathrm{θ}}} \end{gathered}$$

The equation does not match the original equation so the test fails.

the graph may or may not be symmetric with respect to the line$\mathrm{θ}=\frac{\mathrm{π}}{2}$

Substitute$-r$for $r$in the equation

$$\begin{gathered} -r=3^{\mathrm{θ}} \\ r=-3^{\mathrm{θ}} \end{gathered}$$

The equation does not match the original equation so the test fails.

the graph may or may not be symmetric with respect to the pole

Consider different values for $\mathrm{θ}$ and determine coordinates of several points for the graph

Locates points and use them to plot the graph of the equation

The graph state that the equation is a spiral

Plot the graph of the equation$r=3^{\mathrm{θ}}$using a graphing utility

Graph matches so our graph is correct.