Question

How do you use the vertical line test to show `x^2+y^2=25` is a function?

Answer 1

The problem is that `x^2+y^2 = 25` is not a function.

Using the vertical line test with the vertical line
`color(white)("XXXX")` `x=0`
we see that
`color(white)("XXXX")`there are two solutions for `y` (`+5` and `(-5)`)

That is there are two solution points on the vertical line `x=0`
and therefore
`x^2+y^2= 25` is not a function.