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Chapter 1-3 Notes

Chapter 1-3 Notes - Numerical representations table of...

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Source: College Mathematics , Rockswold G., Bennett J., and Briggs W. C:/CLASES_COLEGIO/2007/NOTAS/0102/ 01/12/07 Math 1332 - College Mathematics Chapter 1-3 Notes Functions and Their Representations Function : is a relation in which each element in the domain corresponds to exactly one element in the range. Ex: y = f(x) Function notation: y = f(x) --> f of x equals y f --> name of the function x --> independent variable (input) --> set of valid inputs x , called the domain ( D ) of f y --> dependent variable (output) --> set of corresponding outputs y , called the range ( R ) of f Representations of Functions A function can be represented by verbal descriptions, tables, diagrams, symbols, & graphs (p. 41) Verbal representations - literally describes the function verbally Ex: f(x) = x 3 , “cube the input x”
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Unformatted text preview: Numerical representations- table of values, listing the input-output pairs for a function • Partial numerical representations - “part” of the complete values are listed in a table Diagrammatic representations (diagrams)- visual diagram of a function with domain D and range R , where an arrow shows that x produces y Ex: D R Symbolic representation- a formula Ex: f(x) = x 3 Graphical representation (graph)- visually pairs an x-input with a y-input. Ex: f(x) = x y Identifying Functions By definition of a function, we can determine if a relation is a function. Vertical Line Test- If every vertical line intersects a graph at no more than one point, then the graph represents a function. y Ex: (x-h) 2 + (y-k) 2 = r 2 2 3 4 4 9 16 x x...
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