Question 202574: is y = 3x to the 2 power a relation? a function? is it linear? is it direct variation?
Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! y=3x^2
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Relation, yes, y is related to x
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Function, yes, for every value of x, only one value of y.(obeys vertical line rule)
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Linear, no, x to second power makes it a quadratic(parabola)
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Direct Variation, yes, y is directly related to x^2 by constant 3
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Relation:
A relation between mathematical expressions (such as equality or inequality)
Yep, it is a relation.
Function
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.
Linear Function
A first-degree polynomial function of one variable. Since you have an  it is not a first degree polynomial. It is a second degree polynomial.
Direct Variation
The statement "y varies directly as x," means that when x increases, y increases by the same factor. Here,  varies directly as , so yes it is a direct variation. This is as opposed to having in the numerator on one side of the equals sign and  or some power of in the denominator on the other side, which would be inverse variation.
John
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