Which of the functions shown below are exponential​ functions?

Question

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Part 1
Select all exponential functions.
A.y equals x cubed minus 6 x
y equals x cubed minus 6 x
B.y equals 2 Superscript x
y equals 2 Superscript x
C.y equals x cubed
y equals x cubed
D.y equals 2 x plus 2
y equals 2 x plus 2
E.y equals left parenthesis one fourth right parenthesis Superscript x
y equals left parenthesis one fourth right parenthesis Superscript x
F.y equals one half x Superscript 2 e
y equals one half x Superscript 2 e

Answer 1

To determine which functions are exponential functions, we need to look for functions that can be expressed in the form \( y = a^x \), where \( a \) is a positive constant.

Let's analyze each option:

A. \( y = x^3 - 6x \)
This is a polynomial function, not exponential.

B. \( y = 2^x \)
This is an exponential function because it fits the form \( a^x \) with \( a = 2 \).

C. \( y = x^3 \)
This is also a polynomial function, not exponential.

D. \( y = 2x + 2 \)
This is a linear function, not exponential.

E. \( y = \left( \frac{1}{4} \right)^x \)
This is an exponential function because it fits the form \( a^x \) with \( a = \frac{1}{4} \).

F. \( y = \frac{1}{2} x^2 e \)
This is a polynomial function (specifically a quadratic multiplied by a constant), not exponential.

Based on the analysis, the exponential functions from the options provided are:

B. \( y = 2^x \)
E. \( y = \left( \frac{1}{4} \right)^x \)

So the correct selections are B and E.