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

1 Answer
Jun 13, 2015

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

Explanation:

You can write it as

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

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

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

* ff is smooth and analytic
* f(0)=1f(0)=1,
* f(1)=6f(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)