Question

which of the following is an example of an exponential function?
a. $y = 3x^2$
b. $y = \frac{1}{2x}$
c. $y = 2(3)^x$
d. $y = -2x + 4$

Explanation:

Step1: Recall exponential function form

An exponential function has the form \( y = ab^x \), where \( a
eq 0 \), \( b>0 \), \( b
eq 1 \), and \( x \) is the exponent.

Step2: Analyze Option A

\( y = 3x^2 \) is a quadratic function (variable in the base, exponent is constant), not exponential.

Step3: Analyze Option B

\( y=\frac{1}{2x}= \frac{1}{2}x^{-1} \) is a rational function (power function with negative exponent), not exponential.

Step4: Analyze Option C

\( y = 2(3)^x \) matches \( y = ab^x \) with \( a = 2 \), \( b = 3 \) (satisfies \( b>0, b
eq1 \)), so it's exponential.

Step5: Analyze Option D

\( y=-2x + 4 \) is a linear function (degree 1 polynomial), not exponential.

Answer:

C. \( y = 2(3)^x \)