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

Answer 1

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#.

#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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Answer 2

Kennedy Adams

To determine if the relation │2y│ = 4x defines a function, you need to check if for each value of x, there is only one corresponding value of y.

First, isolate y to express y in terms of x:

If 2y = 4x, then y = 2x. If -2y = 4x, then y = -2x.

So, for every value of x, there are two corresponding values of y: 2x and -2x.

Since there are two possible y-values for some x-values, the relation does not define a function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.