Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$.
$f\left(x\right)=\left(-2\right)^{x}$

• A. Exponential function, $f\left(4\right)=16$
• B. Exponential function, $f\left(4\right)=-16$
• C. Not an exponential function

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the definition of an exponential function. An exponential function is of the form f(x) = a^x, where 'a' is a positive constant and 'x' is the variable exponent.
2. Step 2: Examine the given function f(x) = (-2)^x. Here, the base is -2, which is not a positive constant. This violates the condition for a function to be exponential.
3. Step 3: Consider the implications of having a negative base. When the base is negative, the function does not exhibit the typical properties of exponential growth or decay, especially for non-integer values of x.
4. Step 4: Evaluate the function for x = 4. Substitute x = 4 into f(x) = (-2)^x to get f(4) = (-2)^4. Calculate the result to understand the behavior of the function.
5. Step 5: Conclude that since the base is negative, the function f(x) = (-2)^x is not an exponential function according to the standard definition.