## Vertical line test

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Ridog
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### Vertical line test

Are there any functions/scenarios where the vertical line test does not apply or is incorrect? Feel free to get as complicated as you want/need to.

Example: http://wiki.answers.com/Q/Is_the_graph_ ... a_function

stapel_eliz
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Are there any functions/scenarios where the vertical line test does not apply or is incorrect? Feel free to get as complicated as you want/need to.

Example: http://wiki.answers.com/Q/Is_the_graph_ ... a_function
The question and answer at the link are as follows:
Question: Is the graph of a circle a function?

Answer: Yes, the graph of a circle is a function....

Some people might say that the graph of a circle is not a function, because it violates the single value test, i.e. if you draw a vertical line within the domain of the function, you get more than one value. In fact, however, if you convert the equation from cartesian coordinates to polar coordinates, you pass the single value test, i.e. R is constant for every theta.
Assuming a Cartesian context, the above answer is incorrect, since the Cartesian form is not single-valued, due to the "plus/minus" needed when solving for "y=":

. . . . .$y\, =\, \pm \sqrt{r^2\, -\, x^2}$

The WikiAnswers response seems to assume that, if one can create a functional form on any domain, range, and function definition, the other relational forms are also functions. I am aware of no authority which agrees with this definition of "function".

Ridog
Posts: 2
Joined: Mon Aug 26, 2013 7:12 pm
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### Re: Vertical line test

Interesting, thank you for the clarification!