Step-by-step explanation:
We have [tex]f(x)=y=4^x[/tex] and we need to graph this exponential function.
First we need to find the value of y when x=0, this is:
[tex]f(0)=4^0\\y=1[/tex]
Then the y value when x=0 is y=1. We have then the point (0,1). Which is the point A in the graph.
Now, we have to find the value of y with different values of x:
With x=1:
[tex]f(1)=4^1\\y=4[/tex]
We have the point (1,4). Which is the point B in the graph.
With x=-1:
[tex]f(-1)=4^-^1\\y=\frac{1}{4}=0.25[/tex]
We have the point (-1,0.25). Which is the point C in the graph.
With x=2:
[tex]f(2)=4^2\\y=16[/tex]
We have the point (2,16). Which is the point D in the graph.
With x=-2:
[tex]f(-2)=4^-^2\\y=\frac{1}{16} =0.0625[/tex]
We have the point (-2,0.0625). Which is the point E in the graph.
We can continue calculating y with differents values of x but with 5 points it's enough to graph.
Then the graph of [tex]f(x)=y=4^x[/tex] is:
