Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$ .
$f\left(x\right)=\left(\frac12\right)^{x}$

• A. Exponential function, $f\left(4\right)=\frac{1}{16}$
• B. Exponential function, $f\left(4\right)=-16$
• C. Not an exponential function

Answer: (A)

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 called the base, and 'x' is the exponent.
2. Step 2: Analyze the given function f(x) = (1/2)^x. Here, the base 'a' is 1/2, and the exponent is 'x'. This matches the form of an exponential function.
3. Step 3: Since the function is an exponential function, identify the base and the power. The base is 1/2, and the power is 'x'.
4. Step 4: To evaluate the function for x = 4, substitute 4 into the function: f(4) = (1/2)^4.
5. Step 5: Simplify the expression (1/2)^4 by multiplying 1/2 by itself four times: (1/2) * (1/2) * (1/2) * (1/2). This will give you the value of f(4).