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. Identify the general form of an exponential function, which is f(x) = a^x, where 'a' is a positive constant base and 'x' is the exponent.
2. Examine the given function f(x) = (-2)^x. Here, the base is -2, which is negative.
3. Recall that for a function to be considered exponential, the base 'a' must be a positive real number. Since -2 is negative, this function does not meet the criteria for an exponential function.
4. Evaluate the function at x = 4 to check the behavior: f(4) = (-2)^4. Calculate the power: (-2)^4 = 16, but this step is not necessary for determining if it's exponential.
5. Conclude that since the base is negative, f(x) = (-2)^x is not an exponential function.