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Ch 1.2: Functions

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DEFINITIONS Relation: a set of ordered pairs or 2 quantities related by a rule Function: a relation in which an element of the domain corresponds to EXACTLY ONE element of the range Function Notation: “f(x)”- the value of the function at a given x Piecewise Function: a function defined by 2 or more equations over a specific domain –A.K.A.: Bracket function

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Evaluating functions Plug given value into the function and simplify! Example: g(x) = -3x 2 +2x A) g(4) g(4)= -3(4) 2 +2(4) g(4)= -3(16) + 8 g(4)= - 40 B) g(-5) g(-5)= -3(-5) 2 +2(-5) g(-5)= -3(25) - 10 g(-5)= - 85

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Piecewise Example A. f(4) 4>1, use top expression B. f(-3) -3<1, use bottom expression

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Finding domain and range Determine the limits, if any, on the x and y values If there are no limits, then it is --all Reals Square roots must be positive Can’t be less than 0 Since y equals a square root

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Difference Quotient: (beginning of calculus)

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Functions 2.1 (A). What is a function? Rene Descartes (1637) – Any positive integral power of a variable x. Gottfried Leibniz (1646-1716) – Any quantity.

Functions 2.1 (A). What is a function? Rene Descartes (1637) – Any positive integral power of a variable x. Gottfried Leibniz (1646-1716) – Any quantity.

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