Question

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

Answer 1

This crosses x=1 and does not cross the y-axis. Which choice would it be then?

Answer 2

ANSWER

See graph.


EXPLANATION

The given function is
$f(x) = {4}^{x} .$

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

Since,
$k > \: 0$


the function is an exponential growth function.


Let us look for some few points on this curve.


When
$x = 0$
$f(0) = {4}^{0} .$


$f(0) = 1$

Hence the point
$(0,1)$
lies on this curve and it is the y-intercept.


When
$x = 1$


$f(1) = {4}^{1}$




$f(1) =4$




The point,
$(1,4)$
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.