Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$
$f\left(x\right)={\left(\frac{1}{2}\right)}^x$

• A. Exponential function, $f\left(4\right)=\frac{1}{16}$
• B. Exponential function, $f\left(4\right)=-16$
• C. Not an exponential function
• D. Exponential function, $f\(\left\)(4\(\right\))=2$

Answer: (A)

Verified step by step guidance

1. Identify the form of the given function. An exponential function has the form \(f(x) = b^{x}\), where \(b\) is a positive constant called the base, and \(x\) is the exponent (or power).
2. Look at the given function: \(f(x) = \left(\frac{1}{2}\right)^{x}\). Here, the base \(b\) is \(\frac{1}{2}\), which is a positive number, and the exponent is \(x\).
3. Since the function matches the form \(f(x) = b^{x}\) with a positive base, it is an exponential function.
4. To evaluate the function at \(x=4\), substitute \$4\( for \)x$ in the function: \(f(4) = \left(\frac{1}{2}\right)^{4}\).
5. Simplify the expression \(\left(\frac{1}{2}\right)^{4}\) by raising \(\frac{1}{2}\) to the 4th power, which means multiplying \(\frac{1}{2}\) by itself 4 times.