Can a graph that is in a complete circle possibly have a function
yes
yes definately the formula is
(x - h)² + (y - k)² = r²
plug number in and you get a different sized circle. There are tons of things you can do with this formula...but for your question...simply
YES!
No, a complete circle cannot be represented by a mathematical function. In order to be a function, every input (x-value) must have exactly one output (y-value). However, in a complete circle, each x-value is associated with two different y-values, since there are two points on the circle corresponding to each angle.
To visualize this, imagine drawing a circle on a coordinate plane. If we start from a particular point on the circle, as we move along the circle in a clockwise or counterclockwise direction, we will eventually return to the same point. This means that there are two different y-values for that particular x-value, violating the definition of a function.
Therefore, a graph that forms a complete circle cannot be represented by a single function. It can, however, be represented parametrically using two functions that define the x and y coordinates separately as a function of a parameter, such as the angle theta.