(Conceptual analysis of general exponential curves)

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

Problem

(Conceptual analysis of general exponential curves) (i) State the domain and the range of the function f(x)=abxf(x)=a b^{x} where a≠0a\neq 0 and b>0,  b≠1b>0,\;b\neq 1. (ii) Explain why the xx-axis acts as a horizontal asymptote for every such exponential curve. (iii) Distinguish between exponential growth and exponential decay in terms of the value of the base bb. (iv) Without any numerical calculation, explain whether the graph of f(x)=7(0.8)xf(x)=7(0.8)^{x} can ever meet or cross the xx-axis. Give a reason for your answer.

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