Question 202574
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<b><i>Relation:</i></b>


A relation between mathematical expressions (such as equality or inequality)


Yep, it is a relation.


<b><i>Function</i></b>


The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed set, such as the real numbers (R), although different inputs may have the same output.


The key here is that to be a function, you can never have more than one output for a given input.  The way to tell, in many cases, including this one, is to graph the relation and then see if you can find any vertical line that intersects the graph in more than one point.  If you cannot find such a line, then the relation is a function.


<b><i>Linear Function</i></b>


A first-degree polynomial function of one variable.  Since you have an *[tex \Large x^2] it is not a first degree polynomial.  It is a second degree polynomial.


<b><i>Direct Variation</i></b>


The statement "y varies directly as x," means that when x increases, y increases by the same factor.  Here, *[tex \Large y] varies directly as *[tex \Large x^2], so yes it is a direct variation.  This is as opposed to having *[tex \Large y] in the numerator on one side of the equals sign and *[tex \Large x] or some power of *[tex \Large x] in the denominator on the other side, which would be inverse variation.



John
*[tex \LARGE e^{i\pi} + 1 = 0]
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