If S is a circle with radius 2, why is the upper half of the circle the graph to the function f(x)= (root)(4-x^2) ? What would be the function to the lower half of the circle? (I'm guessing -(root)(4-x^2), but why?)
Thanks!
You're correct. The equation of a circle with radius 2 at the origin is . If you solve this for you get . This isn't a function since there are going to be two values of for every . It doesn't pass the vertical line test. However, you can represent either the top or the bottom as a function by simply defining a function as either or