Mathematics

Problem

Consider the function

h(x)=a^{x-2}+1

, where

0<a<1

. Answer the following, giving full justification: a. (i) Determine the domain of

h

and write the equation of every asymptote of its graph. b. (ii) Find the range of

h

. c. (iii) Calculate the

y

-intercept of the graph of

h

and decide whether the graph possesses an

x

-intercept. Give reasons. d. (iv) Prove that

h

is a decreasing function on its entire domain. e. (v) Solve the equation

h(x)=2

for

x