 # functions.pdf - Functions Function: A function is a...

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FunctionsFunction:A function is a relationship between two variables (one is called independentvariable, another is called dependent variable) such that to each value of the independentvariable there corresponds exactly one value of the dependent variable.Domain of the functiony=f(x):D= The set of all values of the independent variablexfor which the function is defined.Range of the function:R= The set of all values taking on by the dependent variabley.Four ways to represent functions:Verbally: by a description in words;numerically: by a table of values;visually: by a graph{(x, f(x))|xD};algebraically: by an explicit formula.Example 1f(x) =x2x2-3x+2is a function,D={x:x6= 1,2}.Example 2f(x) =4-x2is a function,D={x:-2x2}.Example 3f(x) =±x2is not a function.Example 4Piecewise defined functions:f(x) =(2x,x0;3x,x >0.Example 5Evaluate a function: Letf(x) =x2-2x+ 1. Thenf(5) = 52-2(5) + 1 = 16.f(x+ 3) = (x+ 3)2-2(x+ 3) + 1 =x2+ 4x+ 4.

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Term
Fall
Professor
professor_unknown
Tags
Inverse function, Injective function
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