Question

Which of the following is a power function? Select all correct answers.

1) f(x)=6 ⋅ 16x
2) f(x)=4x√9
3) f(x)=10 ⋅ 3x
4) f(x)=5 ⋅ 15x
5) f(x)=-18x√3

Answer 1

Among the options, only f(x) = 4x√9 and f(x) = -18x√3 are power functions, as they can be expressed with the variable x raised to a constant power.

Step-by-step explanation:

A power function is of the form f(x) = ax^n, where a is a constant and n is a real number. Looking at the options provided, we can determine which ones are power functions. Specifically, a power function is characterized by a variable x raised to a constant exponent.

• 1) f(x) = 6 ⋅ 16^x is not a power function because it involves an exponential function with base 16.
• 2) f(x) = 4x√9 can be simplified to f(x) = 4x· 3, which is a power function with x raised to the first power.
• 3) f(x) = 10 ⋅ 3^x is not a power function due to the exponential term with base 3.
• 4) f(x) = 5 ⋅ 15^x is not a power function because of the exponential term with base 15.
• 5) f(x) = -18x√3 is the same as f(x) = -18x(3^0.5), and since x is to the first power, this is also a power function.

The only answers that represent power functions are therefore f(x) = 4x√9 and f(x) = -18x√3.