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

• A. Exponential function, $f\left(4\right)=16$
• B. Exponential function, $f\left(4\right)=-16$
• C. Not an exponential function
• D. Exponential function, $f\left(4\right)=-8$

Answer: (C)

Verified step by step guidance

1. Recall that an exponential function has the form \(f(x) = b^{x}\) where the base \(b\) is a positive real number (i.e., \(b > 0\)) and the exponent is the variable \(x\).
2. Examine the given function \(f(x) = (-2)^{x}\). Here, the base is \(-2\), which is a negative number.
3. Since the base is negative, this function does not meet the standard definition of an exponential function because exponential functions require a positive base to ensure the function is well-defined for all real \(x\).
4. Therefore, conclude that \(f(x) = (-2)^{x}\) is not an exponential function.
5. Because it is not an exponential function, we do not identify a base and power in the usual sense, nor do we evaluate \(f(4)\) as part of exponential function analysis.