Consider the following four real-valued functions on : f_ 1 (x)=5^ x

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

Problem

Consider the following four real-valued functions on R\mathbb R: f1(x)=5x,f2(x)=(14)x,f3(x)=1x,f4(x)=(−3)x.f_{1}(x)=5^{x}, \qquad f_{2}(x)=\left(\dfrac 14\right)^{x}, \qquad f_{3}(x)=1^{x}, \qquad f_{4}(x)=(-3)^{x}. Answer the questions that follow. (i) For each function, state whether it represents exponential growth, exponential decay, or is not an exponential function according to the standard definition. (ii) Give a brief justification for every classification made in part (i). (iii) For those expressions that are not exponential functions, mention the specific requirement of the definition that they violate.

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