Mathematics

Problem

On the same set of coordinate axes, consider the two functions

f(x)=2^{x}

and

g(x)=\left(\dfrac12\right)^{x}

. Work through the tasks given below. a. (i) Find the

y

–intercept of each function. b. (ii) Sketch the graphs of

f

and

g

on the same axes, clearly labelling the intercepts and the common horizontal asymptote. c. (iii) Using your sketch, compare the numerical values of

f(x)

and

g(x)

for

x=-2,\;0,\;2

. d. (iv) Indicate the point(s) of intersection of the two graphs and explain how your sketch leads to this conclusion.