Determine if the function is an exponential function.  
If so, identify the power & base, then evaluate for $x=4$ .
$f\(\left\)(x\(\right\))=\(\left\)(\(\frac\)12\(\right\))^{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 the base (a positive constant) and 'x' is the exponent (a variable).
2. Step 2: Analyze the given function f(x) = (1/2)^x. Here, the base is 1/2, which is a positive constant, and the exponent is the variable x. This matches the form of an exponential function.
3. Step 3: Identify the base and the power. In this case, the base is 1/2, and the power is x.
4. Step 4: To evaluate the function at x = 4, substitute x = 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 the value of f(4).