Question

Consider `y = f(x) = (x-2) / (x+2)`, does this formula define a function for `-3<x< 3`?

Answer 1

No, the rational expression is undefined when `x = -2`

Explanation:

When `x = -2`, the numerator of `f(x)` is `color(blue)(-2)-2 = -4` while the denominator is `color(blue)(-2)+2 = 0`.

So the formula would say:

`f(-2) = -4/0`

which is undefined, since division by zero is (almost) always undefined.