 ## Tutoring on Determining if a Relations is a Function

Learning Objectives:

#### Understand to Determine if a Relation is a Function.

Math Tutoring on Determining if a Relation is a Function

A function (a set of ordered pair) is a special relationship where each input has a single output. The domain of a function is a set of all possible values for the input variable also known as the independent variable which is often x. The range of a function is a set of all possible values for the output variable or the dependent variable which is often y.   In math tutoring for Vertical Line Test, we imagine a vertical line is drawn through the graph. If the vertical line only touches the graph at one point, then it is a function. If the vertical line touches in more than one point, then it is NOT a function. Think of the vertical line test this way. The points on the graph of a function f have the form (x, f(x)), so once you know the first coordinate, the second is determined. When a vertical line is placed across the graphing plot of this relation, it intersects the graph more than once for some values of x. If a graph shows two or more intersections with a vertical line, then an input (x-coordinate) can have more than one output (y-coordinate).  This is the case when y is not a function of x.

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Hook Questions:

1.    Which graph is a function?

2.    Is a vertical line a linear function?

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