Question

which of the following equations is an exponential function?
○ a. $f(x) = (-3)^x$
○ b. $f(x) = x^2$
○ c. $f(x) = 2^x$
○ d. $f(x) = 5 + 2x$

Explanation:

Step1: Recall exponential function definition

An exponential function has the form $f(x)=b^x$, where $b>0$, $b
eq1$, and $x$ is the variable in the exponent.

Step2: Analyze option a

For $f(x)=(-3)^x$, the base $b=-3<0$, so it does not meet the definition (the function is not real-valued for all real $x$).

Step3: Analyze option b

For $f(x)=x^2$, the variable $x$ is the base, not the exponent. This is a quadratic function, not exponential.

Step4: Analyze option c

For $f(x)=2^x$, the base $b=2>0$ and $b
eq1$, with $x$ as the exponent. This fits the exponential function definition.

Step5: Analyze option d

For $f(x)=5+2x$, this is a linear function (degree 1 polynomial), not exponential.

Answer:

c. $f(x) = 2^x$