Question

Question #9e534

Answer 1

`x^2+y^2=4` is not a function.

Explanation:

While `x^2+y^2=4` is the graph of a circle with radius `2`, it is not a function. A function only has one output for each input. There are several ways to see that this is not the case for a circle. One way to see this is to try to solve for one variable.

Subtracting `x^2` from both sides gives `y^2=4-x^2`.

Taking the square root gives `y=sqrt(4-x^2)` and `y=-sqrt(4-x^2)`, two separate functions. The reason for this is because the square root of a number can be positive or negative. For instance, take `sqrt(4)`. Both `2^2` and `(-2)^2` are equal to `4`. Therefore the square root could be equal to either of them.

Because `x^2+y^2=4` produces two functions, it is not a function, because plugging the same `x` into both equations produces two unique outputs.