Which function grows the fastest for large values of x?

f(x)=1.5x

f(x)=8x

f(x)=3x

f(x)=4x2+3

3 answers

ax^2 grows faster than kx for any a and k you choose.

or, equivalently,

if a > b,
x^a grows faster than x^b
that makes no sense to me
I think the answer is f=1.5x