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:

$f(-2)=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25.$

2.- x=-1, we get:

$f(-1)=2^{-1}=\frac{1}{2}=0.5.$

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: