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Chapter P3 Notes

Chapter P3 Notes - from X to Y is a correspondence that...

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Lauren Nitahara Calculus Notes Chapter P3 - Functions and their Graphs Definition: A relation between two sets X and Y is a set of ordered pairs each of the form (x,y) where x is  in X and y is in Y. Ex: (red, apple) (yellow, banana) Definition: A function  from X to Y is a relation between X and Y that has the property that any two ordered  pairs with the same x-value also have the same y-value. Ex. Is this a function: (green, grapes) (green, apple) Definition: The variable x is the independent variable .     The variable y is the dependent variable . Ex. Circumference of a circle = 2 π r As a function: C(r) = 2 π r r is the independent variable C is the dependent variable Definition: Let X and Y be sets of real numbers.  A real valued function f of real variable x
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Unformatted text preview: from X to Y is a correspondence that assigns to each number x in X exactly one number y in Y. Definition: the domain of f is the set X. Definition: The number y is the image x under f, denoted f(x) = y. Definition: The range of f is a subset of Y and consists of all images of numbers in X. Ex. Consider f(x) = cos(3x). What is f( π /2) ? π /2 is a member of the domain f( π /2) is a member of the range Expressing a Function Implicit Form x 3 + 3y = 4 Explicit Form y = 3(4 – x 3 ) <to solve for y Function Notation f(x) = 3(4 – x 3 ) <most common...
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