Question

What is the x-intercept for the piecewise function `f(x) = x^2-4 , x≥2` and `x-2, x<2`?

Answer 1

The x-intercept is at `x=2`

Explanation:

An x-intercept of a function `f(x)` is a point at which `f(x) = 0`
So, to find the x-intercepts, we look for what values of `x`, if any, fulfill this requirement.

For `x>=2` we have `f(x) = x^2 - 4 = (x+2)(x-2)`

`(x+2)(x-2) = 0 <=> x = -2 or x = 2`

But `-2 < 2` so the only x-intercept for `x >= 2` is at `x=2`

Finally we check for `x<2`

If `x < 2` we have `f(x) = x - 2 = 0 <=> x = 2`

But `2=2` and so there are no x-intercepts where `x < 2`

Thus the only x-intercept of `f(x)` occurs at `x = 2`.