Answer:
The graph in the attached figure
Step-by-step explanation:
we have
![f(x)=2^x](https://tex.z-dn.net/?f=f%28x%29%3D2%5Ex)
This is a exponential function of the form
![y=a(b^x)](https://tex.z-dn.net/?f=y%3Da%28b%5Ex%29)
where
a is the initial value or the y-intercept
b is the base of the exponential function
If b>1 then is a exponential growth function
If b<1 then is a exponential decay function
In this problem
The y-intercept is equal to
For x=0
![f(x)=2^0=1](https://tex.z-dn.net/?f=f%28x%29%3D2%5E0%3D1)
The y-intercept is the point (0,1)
so
![a=1](https://tex.z-dn.net/?f=a%3D1)
![b=2](https://tex.z-dn.net/?f=b%3D2)
The value of b is greater than 1
so
Is a growth function
To plot the graph create a table with different values of x and y
For x=-1
f(x)=2^-1=0.5
point (-1,0.5)
For x=1
![f(x)=2^1=2](https://tex.z-dn.net/?f=f%28x%29%3D2%5E1%3D2)
point (1,2)
For x=2
![f(x)=2^2=4](https://tex.z-dn.net/?f=f%28x%29%3D2%5E2%3D4)
point (2,4)
For x=3
![f(x)=2^3=8](https://tex.z-dn.net/?f=f%28x%29%3D2%5E3%3D8)
point (3,8)
For x=4
f(x)=2^4=16
point (4,16)
Plot the y-intercept and the other points and connect them to graph the exponential function
Note that as x increases the value of y increases (exponential growth function)
The graph in the attached figure