Final answer:
The area of a circle given the circumference can be expressed using the function notation f(C) = π(C / (2π))², where C is the circumference. Substituting C with 117 cm will allow us to calculate the area in cm².
Step-by-step explanation:
To represent the area of a circle using function notation when given the circumference, we first need to understand the relationship between a circle's radius and its circumference. The formula for the circumference C of a circle with radius r is:
C = 2πr
Given the circumference is 117 cm, we can solve for the radius r:
r = C / (2π)
r = 117 cm / (2π)
Once we have the radius, the area A of the circle can be found using the formula:
A = πr²
Using function notation, let's define a function f(C) that represents the area of a circle based on a given circumference C:
f(C) = πr² where r = C / (2π)
Substituting the value of r gives us:
f(117 cm) = π(117 cm / (2π))²
This expression will yield the area of the circle in cm² once calculated.