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

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Answer 1 · 2015-06-08T19:12:36

Any vertical line is described by an equation of the form $x = k$ $x=k$ 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.

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