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Chapter 5: Problem 80

Which functions are exponential? (a) \(3 x\) (b) \(3 x^{2}\) (c) \(3^{x}\) (d) \(2^{-x}\)

Short Answer

Expert verified
(c) \(3^{x}\) and (d) \(2^{-x}\) are exponential functions.

Step by step solution

01

Check function (a)

The function \(3x\) is not an exponential function, because the variable \(x\) is not an exponent, but a base.
02

Check function (b)

The function \(3x^{2}\) is not an exponential function, instead it's a polynomial function, because the variable \(x\) is a base and 2 is the exponent.
03

Check function (c)

The function \(3^{x}\) is an exponential function, because the variable \(x\) is the exponent.
04

Check function (d)

The function \(2^{-x}\) is also an exponential function, because here the variable \(x\) is in the exponent just with a sign change which doesn't change its exponential property.

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