graph the exponential function. (f(x)=2^{x}) plot five points on the graph of the function, and also draw…

Explanation:

Step1: Find points for x = - 2

Substitute x=-2 into $f(x)=2^{x}$, we get $f(-2)=2^{-2}=\frac{1}{4}=0.25$. So the point is $(-2,0.25)$.

Step2: Find points for x = - 1

Substitute x = - 1 into $f(x)=2^{x}$, we get $f(-1)=2^{-1}=\frac{1}{2}=0.5$. So the point is $(-1,0.5)$.

Step3: Find points for x = 0

Substitute x = 0 into $f(x)=2^{x}$, we get $f(0)=2^{0}=1$. So the point is $(0,1)$.

Step4: Find points for x = 1

Substitute x = 1 into $f(x)=2^{x}$, we get $f(1)=2^{1}=2$. So the point is $(1,2)$.

Step5: Find points for x = 2

Substitute x = 2 into $f(x)=2^{x}$, we get $f(2)=2^{2}=4$. So the point is $(2,4)$. The horizontal - asymptote of the exponential function $y = 2^{x}$ is the x - axis, or the line $y = 0$.

Answer:

The five points are $(-2,0.25),(-1,0.5),(0,1),(1,2),(2,4)$ and the horizontal asymptote is $y = 0$.