How do you decide whether the relation #3y - 1 = 7x +2# defines a function?

1 Answer
May 29, 2018

You need to consider the question: Does this relation allow for multiple values of the dependent variable for any value of the independent variable?


For demonstration purposes I will assume that in the given relation: #3y-1=7x+2#, the dependent variable is #y# and the independent variable is #x#.

The given relation can be re-arranged as
and we can see (hopefully this is obvious) that any value of #x# will provide one and only one value for #y#.

Since this was asked under the topic "Functions on a Cartesian Plane", another way to look at this is (assuming you have some way of generating the graph of this relation) is to see if there is any possibility of a vertical line crossing the line of this equation in more than one place:
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In this case we can see that the graph is a straight line, so there can not be any "doubling back" to provide more than one value of #y# for any value of #x#.