Consider the exponential function

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

g(x)=3^{x}

. (i) Using the definition of range, explain why

0

is excluded from the set of values taken by

g(x)

. (ii) Let

h_k(x)=3^{x}+k

, where

k

is a real constant. Explain, without using a graph, how the value of

k

affects the range of

h_k

. (iii) Determine the exact range of

h_{-2}(x)=3^{x}-2

. Give your answer in interval notation and justify each step of your reasoning.