SOLUTION: How can you determine weather a graph is linear and if its a function

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Question 692560: How can you determine weather a graph is linear and if its a function
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If you are given the graph on an x-y plane, and a vertical straight line touches more than 1 point of the graph, y is not a function of x.


If you are given the graph on an x-y plane, and no vertical straight line touches more than 1 point of the graph, y is a function of x.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2F5%2Bx%5E2-2x-5%29

If you are given the graph on an x-y plane, and it is a straight line that is not vertical, y is a linear function of x.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C3x%2F2-1%29

If you are given some sort of definition of an x-y relation, but not the graph, it is a bit more complicated.
If more than one y is assigned to the same x, as in x%5E2%2By%5E2=1, y is not a function of x.
If there is no more than one value of y assigned to each x, as in y=x%5E2 or y=1%2Fx, y is a function of x.
If the relation can be expressed in the form y=mx%2Bb with some constants m and b, y is a linear function of x.