Define the function

MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Define the function

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

. Answer all parts, giving reasons for each conclusion: (i) Determine the domain of

p

. (ii) Find every intercept of the graph of

p

, if it exists. (iii) Obtain the range of

p

. (iv) Write the equation of the horizontal asymptote of the graph of

p

. (v) Describe briefly how the graph of

p

can be obtained from the graph of

y=2^{x}