On a piece of paper graph f(x)=4^x. Then determine which answer matches the graph you drew

ANSWER

See graph.


EXPLANATION

The given function is
[tex]f(x) = {4}^{x} .[/tex]

This is an exponential function of the form,
[tex]f(x) =a {b}^{kx} [/tex]

Since,
[tex]k > \: 0[/tex]


the function is an exponential growth function.


Let us look for some few points on this curve.


When
[tex]x = 0[/tex]
[tex]f(0) = {4}^{0} .[/tex]


[tex]f(0) = 1[/tex]

Hence the point
[tex](0,1)[/tex]
lies on this curve and it is the y-intercept.


When
[tex]x = 1[/tex]


[tex]f(1) = {4}^{1} [/tex]




[tex]f(1) =4[/tex]




The point,
[tex](1,4)[/tex]
also lies on this curve. So the graph of this curve must go through this point.



Now as x-values approaches negative infinity the function approaches zero.


We can use this information to obtain the graph in the attachment.