Consider the cubic function and the exponential function .

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Consider the cubic function

f(x)=x^3

and the exponential function

g(x)=2^x

. (i) Find the

y

-intercept of each function and state whether either function possesses symmetry about the

y

-axis or the origin. (ii) Sketch the graphs of

f

and

g

on the same set of axes for

-3\le x\le 3

, clearly labelling the curves. (iii) Using your sketches or otherwise, explain which of the two functions grows faster as

x\to \infty

and which grows faster as

x\to -\infty

. (iv) Give a reasoned argument, without using calculus, to support the conclusions reached in part (iii).