Answer
Graph of $f(x)=\left(\dfrac{1}{5}\right)^x$
Work Step by Step
Substituting values of $x$ in the given function, $
f(x)=\left(\dfrac{1}{5}\right)^x
$, results to
\begin{array}{c|c|c}
\text{If }x=-1: & \text{If }x=0 & \text{If }x=1
\\\\
f(x)=y=\left(\dfrac{1}{5}\right)^x & f(x)=y=\left(\dfrac{1}{5}\right)^x & f(x)=y=\left(\dfrac{1}{5}\right)^x
\\
y=\left(\dfrac{1}{5}\right)^{-1} & y=\left(\dfrac{1}{5}\right)^0 & y=\left(\dfrac{1}{5}\right)^1
\\\\
y=5 & y=1 & y=\dfrac{1}{5}
.\end{array}
Tabulating the results above results to the table below.
\begin{array}{c|c}
\hline
x & y
\\\hline
-1 & 5
\\\hline
0 & 1
\\\hline
1 & \dfrac{1}{5}
\end{array}
Connecting the points $
\left(-1,5\right),
\left(0,1\right),
\text{ and }
\left(1,\dfrac{1}{5}\right)
$ with a curve gives the graph of $
f(x)=\left(\dfrac{1}{5}\right)^x
$.
