Precalculus Functions and Graphs
Graphs of Functions Concepts 1

|  |  | Definition 1 |  |
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A function is a correspondence (or rule) that assigns to each member of some set called the domain exactly one member of a set called the range .

|  |  | Definition 2 |  |
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Let the domain and the range of the function be the sets of real numbers. The graph of the function is the set of all ordered pairs (x, f(x)) in the plane for all members x from the domain.

To graph a function, we find ordered pairs (x, f(x)), plot them and connect the points.

x | f(x)
-5 | -10
-2.5 | -5
2.5 | 5
5 | 10

If a vertical line drawn anywhere on the graph intersects the curve in more than one point, then there will be more than one number in the range corresponding to a member of the domain. The graph is not the graph of a function.

The Vertical Line Test If it is possible for a vertical line to intersect a graph more than once the graph is not the graph of a function.

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