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. Identify the exponential function you need to evaluate. An exponential function generally has the form \(f(x) = a^{x}\), where \(a\) is the base and \(x\) is the exponent.
2. Substitute the given value of \(x\) into the function. For example, if you need to evaluate \(f(3)\), replace \(x\) with 3 in the expression \(a^{x}\) to get \(a^{3}\).
3. Calculate the power by multiplying the base \(a\) by itself \(x\) times. For instance, \(a^{3} = a \times a \times a\).
4. If the exponent is zero, recall the rule that any nonzero base raised to the zero power equals 1, i.e., \(a^{0} = 1\).
5. If the exponent is negative, use the rule \(a^{-x} = \frac{1}{a^{x}}\) to rewrite the expression as a reciprocal with a positive exponent before evaluating.