Question

In the following exercises,graph each of the following functions.

$f\left(x\right)={\left(\frac{1}{5}\right)}^x$.

Short answer

The result will be the graph of $f\left(x\right)={\left(\frac{1}{5}\right)}^x$ as shown below

Step-by-step solution

Step 1.Given information

Consider the given quadratic equation $f\left(x\right)={\left(\frac{1}{5}\right)}^x$

To draw the graph,choose some random value(negative,positive or zero) for x and substitute them into the equation and to find$f\left(x\right)$

Step 2.Record the value of ordered pair in the table as shown below.

x	$f\left(x\right)={\left(\frac{1}{5}\right)}^x$	$\left(x,f\left(x\right)\right)$
-2	role="math" localid="1645083735609" ${\left(\frac{1}{5}\right)}^{-2}=25$	$\left(-2,25\right)$
-1	${\left(\frac{1}{5}\right)}^{-1}=5$	$\left(-1,5\right)$
0	${\left(\frac{1}{5}\right)}^0=1$	$\left(0,1\right)$
1	${\left(\frac{1}{5}\right)}^1=\frac{1}{5}$	$\left(1,\frac{1}{5}\right)$
2	${\left(\frac{1}{5}\right)}^2=\frac{1}{25}$	role="math" localid="1645083932592" $\left(2,\frac{1}{25}\right)$

Step 3.Now plot ordered pair listed in the third column and connect them with a smooth curve.

The result will be the graph of $f\left(x\right)={\left(\frac{1}{5}\right)}^x$as shown below.