Question

How do you graph `f(x) = 6^x`?

Answer 1

graph{6^x [-10, 10, -5, 5]}

Explanation:

You can write it as

`exp(xln(6))` (in my notation, `exp(x)=e^x=sum_(n=0)^(+infty)(x^n)/(n!)`)

`ln(6)>0 => f(x)~exp(x)`

So you have, from the properties of the exponential function.

`* f` is smooth and analytic
`* f(0)=1`,
`* f(1)=6`,
`* f(x)->0 if x->-infty`
`* f(x) -> +infty if x->+infty` more quickly than any polynomial.
`* f`is always increasing

Using this information you can draw the graph as in figure

(Notice that if you have had a base `<1`, you would have had `f(x)~exp(-x)`, and the graph would have been specular)