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

1 Answer
George C.
Jun 8, 2015

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.

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