Question

Which of the following are exponential functions? Select all correct answers.

Select all that apply:

f(x)=8(14)^x
g(x)=13(1.97)^x
h(x)=12(1/8)^x
j(x)=5(−1/3)^x
k(x)=11(−15)^x

Answer 1

Exponential functions have a form of f(x) = ab^x with 'a' as a nonzero constant and 'b' as a positive number not equal to 1. Applying this to the given functions, f(x), g(x), and h(x) are exponential because their bases are positive real numbers. Functions j(x) and k(x) are not because their bases are negative.

Step-by-step explanation:

An exponential function is generally defined as any function of the form f(x) = abx, where a is a nonzero constant, b is a positive real number not equal to 1, and x is any real number. For the functions provided in the question, we will apply this definition to determine which are exponential:

• f(x) = 8(14)x is exponential because 14 is a positive real number greater than 1.
• g(x) = 13(1.97)x is exponential because 1.97 is a positive real number greater than 1.
• h(x) = 12(1/8)x is exponential because 1/8 is a positive real number, although less than 1, it is allowed since it represents decay.
• j(x) = 5(−1/3)x is not exponential because the base, -1/3, is negative.
• k(x) = 11(−15)x is not exponential because the base, -15, is negative.

Therefore, functions f(x), g(x), and h(x) are exponential functions.