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Learn about relations and functions through ordered pairs, domain, range, and graphs. Understand how to distinguish functions using the vertical line test. Practice examples to solidify your knowledge.
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Lesson 8.1 Use graphs to represent relations and functions
Relation – a pairing of numbers in one set with numbers in another set • Domain (x) – the set of all possible inputs for the relation • Range (y) – the set of all possible outputs for the relation • *a relation can be represents by ordered pairs. x-value is the domain and the y-value is the range.
Domain and Range • What is the domain and range? Example: (0,1) (2,4) (3,7) (5,4) 1.) (-1,2) (-3,-1) (6,0) (-1,4)
Representing Relations – relations can be ordered pairs, set up in a table, a graph or by mapping. Ex: (2,0) (1,-1) (2,2) (0,0) (-1,1) 2.) Represent (3,2) (2,4) (1,-2) (0,-3) (3,-1) as a relation in a graph and mapping.
Function – a relation is a function if for input there is exactly one output Tell whether the relation is a function Ex: (0,3) (1,2) (2, -1) (4,4) (5,4) 3.) (-2,-1) (0,2) (2,3) (-2,-4) 4.) (2,5) (4,7) (6,5) (8,7) 5.) (2,9) (4, 11) (2,10)
Vertical Line Test – if you can find a vertical line passing through more than one line in a graph, then the relation is not a function Ex: Ex:
