Question

Graph the exponential function f(x) = 2 ^ x Plot five points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Answer 1

To plot the function, first, we determine five points on the graph. To determine the points we evaluate the function at

`x=-2,-1,0,1,2.`

Evaluating the function at:

1.- x=-2, we get:

`f(-2)=2^(-2)=(1)/(2^2)=(1)/(4)=0.25.`

2.- x=-1, we get:

`f(-1)=2^(-1)=(1)/(2)=0.5.`

3.- x=0, we get:

`f(0)=2^0=1.`

4.- x=1, we get:

`f(1)=2^1=2.`

5.- x=2, we get:

`f(2)=2^2=4.`

Now, notice that as

`x\rightarrow\infty,`
`f(x)\rightarrow0.`

Therefore, f(x) has a horizontal asymptote at y=0.

Answer: