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ANSWER:

In a function, the relation between  x and y-values can be modelled as a graph, algebra and the table of values.  Yet, each value of x corresponds to only one value of y.  Algebraically, function can be expressed using the function notation, f(x) instead of using y,  the input of the function is x and output of the function is y.  Also, the equation involves more than one variable.  When the function is graphed, it needs to pass the vertical line test.

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The Vertical Line Test:

It is used to determine whether the graph is a function.  When the graph is a function, it only intersects once with the vertical line, y=x.  When the graph is not a function, it intersects twice with any vertical line.

・Only one intersection・

・Passes the Vertical Line Test・

・Function・

                    2

f(x)=x

 

・Two intersections・

・Does NOT pass the Vertical Line Test・

・NOT a Function・

                    2      2

f(x)=x+ y

 

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