Answer:
See the graph and explanation below.
Step-by-step explanation:
For this case we have the following function:
[tex] f(x) = e^{-\frac{x}{3}}[/tex]
We can calculate some points in order to see the tendency of the graph, we can select a set of points for example [tex] x =-2,-1.5,-1,0,1,1,5,2[/tex] and we can calculate the values for f(x) like this
x=-2
[tex] f(x=-2) =e^{-\frac{-2}{3}}= e^{\frac{2}{3}}=1.948[/tex]
x=-1.5
[tex] f(x=-1.5) =e^{-\frac{-1.5}{3}}= e^{0.5}=1.649[/tex]
x=-1
[tex] f(x=-1) =e^{-\frac{-1}{3}}= e^{\frac{1}{3}}=1.396[/tex]
x=0
[tex] f(x=0) =e^{-\frac{0}{3}}= e^{0}=1[/tex]
This point correspond to the y intercept.
x=1
[tex] f(x=1) =e^{-\frac{1}{3}}=0.717[/tex]
x=2
[tex] f(x=2) =e^{-\frac{2}{3}}=0.513[/tex]
We don't have x intercepts for this case since the function never crosses the x axis.
And then we can see the plot on the figure attached.
