Question

Question 3. Y=(1/5)^xSketch the graph of each of the exponential functions and label three points on each graph.

Answer 1

Given exponential function:

$y\text{ = (}\frac{1}{5})^x$

Let us obtain three points including the y-intercept so that we can plot the function y = f(x)

When x =0:

$\begin{gathered} y\text{ = (}\frac{1}{5})^0 \\ =\text{ 1} \end{gathered}$

when x =1:

$\begin{gathered} y\text{ = (}\frac{1}{5})^1 \\ =\text{ }\frac{1}{5} \end{gathered}$

when x =2:

$\begin{gathered} y\text{ = (}\frac{1}{5})^2 \\ =\text{ }\frac{1}{25} \end{gathered}$

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: