To plot the function, first, we determine five points on the graph. To determine the points we evaluate the function at
[tex]x=-2,-1,0,1,2.[/tex]
Evaluating the function at:
1.- x=-2, we get:
[tex]f(-2)=2^{-2}=\frac{1}{2^2}=\frac{1}{4}=0.25.[/tex]
2.- x=-1, we get:
[tex]f(-1)=2^{-1}=\frac{1}{2}=0.5.[/tex]
3.- x=0, we get:
[tex]f(0)=2^0=1.[/tex]
4.- x=1, we get:
[tex]f(1)=2^1=2.[/tex]
5.- x=2, we get:
[tex]f(2)=2^2=4.[/tex]
Now, notice that as
[tex]x\rightarrow\infty,[/tex][tex]f(x)\rightarrow0.[/tex]
Therefore, f(x) has a horizontal asymptote at y=0.
Answer:
