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

1 Answer
Alberto M.
Jun 13, 2015

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)

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