An exponential function is denoted by

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

Problem

f(x)=a\,b^{x}

, where

a\ne 0

b>0

and

b\ne 1

. Answer the following questions related to this general form. (i) Define an exponential function and state its domain and range. (ii) Prove that the

y

-intercept of the graph of an exponential function

f(x)=a\,b^{x}

(0,a)

. (iii) Let an exponential function pass through its

y

-intercept

(0,a)

and an additional point

(x_{1},y_{1})

with

x_{1}\ne 0

. Show algebraically that

b=\left(\dfrac{y_{1}}{a}\right)^{1/x_{1}}