Question

Is a circle a function? Explain why or why not.

Short answer

No, the circle is not a function. It is an equation and it consists of upper function and a lower function.

It does not pass the vertical line test to be a function.

Step-by-step solution

Step 1. To explain

To explain if circle is the function

Step 2. Reason for circle is not a function

A circle is not a function.

The mathematical formula used to describe a circle is an equation, not one function.

For a given set of inputs a function must have at most one output.

A circle consists of two functions, so it is an equation and not a function

Step 3. Vertical line test.

Consider a circle with radius $r$and the center $(h,k)$

The circle does not pass the vertical line test, so it is not a function.