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

Jun 13, 2015

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

#### Explanation:

You can write it as

$\exp \left(x \ln \left(6\right)\right)$ (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.

$\cdot f$ is smooth and analytic
$\cdot f \left(0\right) = 1$,
$\cdot f \left(1\right) = 6$,
$\cdot f \left(x\right) \to 0 \mathmr{if} x \to - \infty$
$\cdot f \left(x\right) \to + \infty \mathmr{if} x \to + \infty$ more quickly than any polynomial.
$\cdot f$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)