Question

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

Answer 1

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(0)=4^0=1`
`x=1` that gives you `y=f(1)=4^1=4`
`x=2` that gives you `y=f(2)=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(-1)=4^-1=1/4=0.25`
`x=-2` that gives you `y=f(-2)=4^-2==1/4^2=1/16=0.06`
less than this will be difficult to plot consistently with the other points.
Graphically: