Question

Graphing an exponential function and its asymptote: f(x)=b-x or f(x)=-bax

Answer 1

Given:

`f(x)=-3^(-x)`

To plot five points on the graph, we input any values of x into the given function.

Example:

Let x=2

So,

`\begin{gathered} f(x)=-3^(-x) \\ =-3^(-2) \\ =-(1)/(9)\text{ or -0.1111} \end{gathered}`

Thus, the point is (2,-1/9).

Let x=1:

`\begin{gathered} f(x)=-3^(-x) \\ =-3^(-1) \\ =-(1)/(3)\text{ or -0.3333} \end{gathered}`

Thus, the point is (1,-1/3).

Let x=0

`\begin{gathered} f(x)=-3^(-x) \\ =-3^(-0) \\ =-1 \end{gathered}`

Thus, the point is (0,-1).

Let x=-1

`\begin{gathered} f(x)=-3^(-x) \\ =-3^(-(-1)) \\ =-3 \end{gathered}`

Thus, the point is (-1,-3).

Let x=-0.5

`\begin{gathered} f(x)=-3^(-x) \\ =-3^(-(-0.5)) \\ =-1.732 \end{gathered}`

Thus, the point is (-0.5,-1.732).

Then, to get the asymptote, we use