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. First, understand what an exponential function is. An exponential function is of the form \( f(x) = a^x \), where \( a \) is a constant base and \( x \) is the exponent.
2. Examine the given function \( f(x) = \left( \frac{1}{2} \right)^x \). This matches the form of an exponential function, where the base \( a \) is \( \frac{1}{2} \) and the exponent is \( x \).
3. Since the function is an exponential function, identify the base and the power. Here, the base is \( \frac{1}{2} \) and the power is \( x \).
4. To evaluate the function for \( x = 4 \), substitute \( x = 4 \) into the function: \( f(4) = \left( \frac{1}{2} \right)^4 \).
5. Calculate \( \left( \frac{1}{2} \right)^4 \) by multiplying \( \frac{1}{2} \) by itself four times: \( \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \). This will give you the value of \( f(4) \).