Definition of Exponential Function

[nycmathguy]

Section 3.1

Questions:

1. Why are exponential functions always raised to a variable?

2. In the definition above, f(x) = a^(x) represents an exponential function.

A. Why must a be greater than 0?

B. Why can't a = 1?

 

[MathLover1]

1. Why are exponential functions always raised to a variable?
by definition, exponential functions a function whose value is a constant raised to the power of the argument

2. In the definition above, f(x) = a^(x) represents an exponential function.
yes
A. Why must a be greater than 0?
because if a=0, than f(x) = a^(0)=1
the exponential function can not be negative, nor equal to zero, because for some exponents the function would not be defined

B. Why can't a = 1?

if a=1 than f(x) = a^1=a which is a horizontal line

 

[nycmathguy]

1. Why are exponential functions always raised to a variable?
by definition, exponential functions a function whose value is a constant raised to the power of the argument

2. In the definition above, f(x) = a^(x) represents an exponential function.
yes
A. Why must a be greater than 0?
because if a=0, than f(x) = a^(0)=1
the exponential function can not be negative, nor equal to zero, because for some exponents the function would not be defined

B. Why can't a = 1?

if a=1 than f(x) = a^1=a which is a horizontal line

Interesting. Thank you.