Which of the functions shown below are exponential​ functions?

Question

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Part 1
Select all exponential functions.
A.y equals 4 x plus 1
y equals 4 x plus 1
B.y equals 2 Superscript x
y equals 2 Superscript x
C.y equals x squared minus 4 x
y equals x squared minus 4 x
D.y equals x Superscript 4
y equals x Superscript 4
E.y equals left parenthesis one half right parenthesis Superscript x
y equals left parenthesis one half right parenthesis Superscript x
F.y equals one half x Superscript 2 e
y equals one half x Superscript 2 e

Answer 1

To identify the exponential functions from the given options, it’s important to recognize the form of an exponential function. An exponential function has the general form:

\[ y = a \cdot b^x \]

where \( a \) is a constant, \( b \) is the base (a positive real number), and \( x \) is the exponent.

Now let's examine each option:

A. \( y = 4x + 1 \) - This is a linear function, not exponential. B. \( y = 2^x \) - This is an exponential function. C. \( y = x^2 - 4x \) - This is a quadratic function, not exponential. D. \( y = x^4 \) - This is a polynomial function, not exponential. E. \( y = \left(\frac{1}{2}\right)^x \) - This is an exponential function. F. \( y = \frac{1}{2} x^2 e \) - This is not in exponential form; it is a polynomial multiplied by a constant.

Thus, the exponential functions from the given options are:

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

The correct answers are B and E.