How do you decide whether the relation #│2y│ = 4x# defines a function?

1 Answer
A. S. Adikesavan
Apr 6, 2016

This defines x as a single-valued function of y for all values of y. #x>=0#. The graph is the pair of radial lines, from the origin, in the 1st and 4th quadrants, with slopes #+-2#.

Explanation:

#x>=0#. The equation can be separated into #x = -2y#, y<0 and x=2y, y>0.
x is a single-valued function of y. For every x > 0, there are two #+-y#. values.
The graph is the pair of radial lines, from the origin, in the 1st and 4th quadrants, with slopes #+-2#.

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