Question

How do you use the vertical line test to show `y=abs(x-3)+abs(x-1)` is a function?

Answer 1

Any vertical line is described by an equation of the form `x=k` for some `k in RR`.

If you substitute this equation into the given equation you get:

`y_k = abs(k-3)+abs(k-1)`

This describes a unique point of intersection `(k, y_k)` between `x=k` and the curve described by the equation `y = abs(x-3)+abs(x-1)`

The vertical line test is satisfied: No vertical line intersects the curve described by the equation `y = abs(x-3)+abs(x-1)` at more than one point.