Functions and Mappings - *Functions You all already have a...

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* Functions
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You all already have a pretty good instinctive understanding of what functions are Mathematical rules for connecting inputs and outputs
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2 1 0 -1 -2 6 5 4 3 2 1 0 Case (i) Notice that each element of A maps to one and only one element of B. A B This is called a one-to-one mapping
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2 1 0 -1 -2 6 5 4 3 2 1 0 Case (ii) Notice that two elements of A maps to one element of B. A B This is called a two-to-one mapping or many-to-many mapping.
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A one-to-one mapping or a many-to-one mapping is called a function. We don’t usually think of it like this though We think about functions like this Example : Case (i) the rule is ‘add 4’ Case (ii) the rule is ‘square x It’s usually helpful to think of functions in terms of inputs and outputs Where is usually the input and is usually the output f ( x ) = x + 4 y = x 2
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* Different ways to write a function There are several different but equivalent ways of writing a function. E.g. the function that maps x on to x 2 can be written in any of the following ways. Read this as f maps x onto x 2 2 y x 2 ( ) f x x 2 : f x x
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The Vertical line test If a vertical line can cut the curve more than once ANYWHERE, then it is NOT a function
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Linear and Non-linear functions or Is an example of a linear function The important thing is that ANY terms ONLY has an exponent of 1 Example ( “a” is a constant) Is linear IS NOT A LINEAR FUNCTION
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You remember how to find the equations of straight lines? Of course you do a) Find the equation of the straight line that has a gradient of -1 and goes through the point () and now you can just sub in the x and y coordinate
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