Understanding Functions in Mathematics
Recap on functions in mathematics, including domains, codomains, ranges, types of functions, and the Vertical Line Test to determine if a relation is a function. Explore examples and illustrations to enhance comprehension.
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LCHL Strand 5 Functions: Relations and Functions Recap of functions and Vertical Line test for Functions Culan O Meara Ballinrobe Community School
Recap: Functions Domain: The set of input values. For example: {1,2,3,4} Codomain: The set of possible outputs. For example: the set of Real numbers Range: The set of actual outputs. For example: If f(x)=2x and the Domain and Codomain are as above, the Range would be {2,4,6,8} In function notation, you will see ?:? ? or similar. This tells us that both the Domain and Codomain are Reals Author: Culan O'Meara
Recap: Functions To qualify as a function, a relation must map every input to a unique output Different types One-to-one. Example: f x = x + 1. Do all inputs map to a unique output? Yes Many-to-one. Example: f x = ?2. Both 2 and - 2 map to 4. Do all inputs map to a unique output? Yes Author: Culan O'Meara
Recap: Functions You can have a relation that is not a function. Any circle is not a function because one input can be mapped to more than one output This is an example of a One-to-many case. Where this exists, it is not a function Author: Culan O'Meara
Vertical Line test When you are given a graph of a relation and you need to determine whether it s a function or not, you can use the Vertical Line Test If you draw a vertical line through various parts of the relation(as shown) and your line crosses it more than once, then it is a one-to- many relationship which is not a function In the diagram, this is NOT a function Author: Culan O'Meara
Vertical Line test In the diagram, this IS a function At no point do any of our vertical lines cross the graph more than once It s the trigonometric function 20sin(x) Author: Culan O'Meara
Vertical Line test In the diagram, this IS a function At no point do any of our vertical lines cross the graph more than once It s the quadratic function ?2 10 or 1 10?2 Author: Culan O'Meara
