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 * b^x, where 'a' is a constant, 'b' is the base (a positive real number not equal to 1), and 'x' is the exponent.
2. Step 2: Analyze the given function f(x) = (-2)^x. Here, the base is -2, which is a negative number. Recall that for a function to be exponential, the base must be a positive real number.
3. Step 3: Conclude that since the base (-2) is negative, the given function does not meet the criteria for an exponential function.
4. Step 4: Note that evaluating f(4) = (-2)^4 would result in a positive value (16), while evaluating f(4) = (-2)^4 with a negative base raised to an odd power would result in a negative value. This inconsistency further supports that the function is not exponential.
5. Step 5: Final conclusion: The given function f(x) = (-2)^x is not an exponential function because the base is negative, which violates the definition of an exponential function.