Given exponential function:
[tex]y\text{ = (}\frac{1}{5})^x[/tex]
Let us obtain three points including the y-intercept so that we can plot the function y = f(x)
When x =0:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^0 \\ =\text{ 1} \end{gathered}[/tex]
when x =1:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^1 \\ =\text{ }\frac{1}{5} \end{gathered}[/tex]
when x =2:
[tex]\begin{gathered} y\text{ = (}\frac{1}{5})^2 \\ =\text{ }\frac{1}{25} \end{gathered}[/tex]
We have the points : (0, 1), (1, 1/5), and (2, 1/25)
Using these points, let us provide a sketch of the plot of y =f(x). We have the plot as shown below:
