Question

consider the relation below

1.Is the relation A function
2. Is the relation a one to one function
3. Is the inverse of the relation below itself a function

Answer 1

Answers:

1. Yes it's a function.
2. No, the function is not one-to-one.
3. No, the inverse isn't a function.

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Step-by-step explanation:

We have a function since the curve passes the vertical line test. Recall that this test is where we try to draw a single vertical line through more than on point on the curve. Such a task isn't possible in this case.

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On the other hand, the curve does not pass the horizontal line test. It is possible to draw a single horizontal line through more than one point on the curve.

This function is not one-to-one since it does not pass the horizontal line test.

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Because the graph isn't one-to-one, the inverse won't be a function. The process of finding the inverse involves swapping x and y; which means we swap from "horizontal line test" to "vertical line test".

The original function failing the horizontal line test would mean the inverse fails the vertical line test.