Question

Graph the exponential function.g(x) = (4/5)^xPlot five points on the graph of the function. Then click on the graph-a-function button.

Answer 1

ANSWER

EXPLANATION

We want to graph the given exponential function:

$g(x)=(\frac{4}{5})^x$

To do this, we have to find 5 points that lie on the graph.

Let us solve the function for x = -6, -3, 0, 3, 6:

$\begin{gathered} \Rightarrow x=-6: \\ g(-6)=(\frac{4}{5})^{-6}=3.81 \\ \Rightarrow x=-3: \\ g(-3)=(\frac{4}{5})^{-3}=1.95 \\ \Rightarrow x=0: \\ g(0)=(\frac{4}{5})^0=1 \\ \Rightarrow x=3: \\ g(3)=(\frac{4}{5})^3=0.51 \\ \Rightarrow x=6: \\ g(6)=(\frac{4}{5})^6=0.26 \end{gathered}$

Now, we have five points to plot the graph with:

$\begin{gathered} (-6,3.81) \\ (-3,1.95) \\ (0,1) \\ (3,0.51) \\ (6,0.26) \end{gathered}$

Let us now plot the points and join the line:

That is the graph of the function