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: 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 'a' must be a positive real number. Since -2 is negative, f(x) = (-2)^x does not meet the criteria for an exponential function.
4. Step 4: Evaluate the function at x = 4 to check consistency. Calculate f(4) = (-2)^4. This involves raising -2 to the power of 4.
5. Step 5: Conclude that since the base is negative, f(x) = (-2)^x is not an exponential function, and therefore, the correct answer is 'Not an exponential function'.