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 exponent.
2. Step 2: Analyze the given function f(x) = (-2)^x. Here, the base 'a' is -2, which is negative.
3. Step 3: Recall that for a function to be considered exponential, the base must be a positive real number. Since -2 is negative, this function does not meet the criteria for an exponential function.
4. Step 4: Evaluate the function at x = 4 to see if it behaves like an exponential function. Calculate f(4) = (-2)^4.
5. Step 5: Since the base is negative, the function does not consistently produce real number outputs for all real x, confirming it is not an exponential function.