Question

Graphing Natural Exponential Functions In Exercise,sketch the graph of the function.See Example 1.

g(x) = e1-x

Answer 1

See the graph and explanation below.

Explanation:

For this case we have the following function:

`f(x) = e^(1-x)`

We can calculate some points in order to see the tendency of the graph, we can select a set of points for example
`x =-2,-1.5,-1,0,1,1,5,2` and we can calculate the values for f(x) like this

x=-2

`f(x=-2) =e^(1+2)= e^(3)=20.086`

x=-1.5

`f(x=-1.5) =e^(1+1.5)= e^(2.5)=12.182`

x=-1

`f(x=-1) =e^(1+1)= e^(2)=7.389`

x=0

`f(x=0) =e^(1-0)= e^(1)=2.718`

This point correspond to the y intercept.

x=1

`f(x=1) =e^(1-1)= e^(0)=1`

x=2

`f(x=2) =e^(1-2)= e^(-1)=0.368`

We don't have x intercepts for this case since the functionnever crosses the x axis.

And then we can see the plot on the figure attached.