The exponential function form f(x)=a^x

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Question from Lucy, a student:

Hi,
Why does the "a" value in the exponential function form f(x)=a^x have to be negative?

Hi Lucy,

$a$ certainly does not need to be negative. For example in the exponential function $f(x) = 5^x, a = 5.$ If $a$ is negative you need to take some extra care however. If $a = -3$ then the function $f(x) = a^x$ has the value at $x = 2$ of $f(2) = a^2 = (-3)^2 = 9$ while $-3^2 = - (3)^2 = -9.$

Penny

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