Mathematics

Problem

A continuous function

y=f(x)

satisfies the following properties: (i)

f(0)=1

; (ii)

f(x)>0

for all real

x

; (iii)

\displaystyle \lim_{x\to\infty}f(x)=\infty

and

\displaystyle \lim_{x\to -\infty}f(x)=0

; (iv)

f(a+b)=f(a)\,f(b)

for all real numbers

a

and

b

. Based on these conditions,

f(x)

is most likely an example of which parent function? a) Logarithmic function b) Exponential function c) Quadratic function d) Modulus (absolute‐value) function

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