# How do you graph: f(x)=4^x?

Jul 25, 2015

This is an exponential function:

#### Explanation:

In general your function will ALWAYS give you positive $y$ values so the graph will be only in the first and second quadrant (forget about the negative $y$ axis).
To plot the graph I would use "interesting" values as:
$x = 0$ that gives you $y = f \left(0\right) = {4}^{0} = 1$
$x = 1$ that gives you $y = f \left(1\right) = {4}^{1} = 4$
$x = 2$ that gives you $y = f \left(2\right) = {4}^{2} = 16$

for the negative $x$ I have to be careful because the value of $y$ will become very small quite quickly so I try:
$x = - 1$ that gives you $y = f \left(- 1\right) = {4}^{-} 1 = \frac{1}{4} = 0.25$
$x = - 2$ that gives you $y = f \left(- 2\right) = {4}^{-} 2 = = \frac{1}{4} ^ 2 = \frac{1}{16} = 0.06$
less than this will be difficult to plot consistently with the other points.
Graphically: