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Unformatted text preview: Obj 9 CenterRadius Form of the Equation of a Circle x y Identify the center and radius. ( x − 3) 2 + ( y − 2) 2 = 25 ( x − 2) 2 + ( y + 1) 2 = 5 x 2 + ( y + 3) 2 = 4 Objective 10 Functions A function is an algebraic rule (or a correspondence between sets) that associates each element, x , from one set with a element, y , of another set. The set of x ’s is the . The set of y ’s is the . Obj 10a Identify a Function (from graph or set of points) Consider x 2 + y 2 = 4. The graph of a function must pass the x y 1 Which represent the graph of a function? (Read carefully; sometimes we ask “Which do not represent the graph of a function?”) y x y x y x Which are functions? { (1 , 2) , (3 , 2) , (5 , − 3) } { (1 , 2) , (1 , − 2) , ( − 1 , 3) } —————————————————————————————————————– Obj 10b Function Notation; Evaluate a function Instead of writing y = 3 x 2 − 5 x + 8, we now write f ( x ) = 3 x 2 − 5 x + 8 Instead of saying “let x = 2, find y ”, we now write f (2) Find each of the following for the functions given below. f ( x ) = 3 x 2 − 5 x + 8 g ( x ) = 3 − x 2 h ( x ) =  3 − 5 x  m ( x ) = x n ( x ) = 2 f ( x − 2) = g ( − 1) = g (2 a ) = g ( x + h ) = h (1) = h ( − 3) = m ( − 3) = m (5) = n ( − 3) = n (5) = m (2 a ) = m ( x + h ) = n (2 a ) = n ( x + h ) = 2 Obj 10c Domain and Range Give Domain and Range (from the graph of a function.) x y x y x y More Obj 10c  Give Domain (only) from the function rule. We’re being asked for the set of real numbers that can be substituted in for . What prevents a value from being plugged in for x ? When might the domain not be “all real numbers”? There are only TWO situations that limit (restrict) the values that can be used for x : Give the Domain f ( x ) = 3 x 7 + 5 x 4 + √ 5 g ( x ) =  3 − 5 x  +17 h ( x ) = 3 √ 1 − x f ( x ) = √ 3 x + 7 3 Some eGrade problems ask: For f ( x ) = √ 3 x + 7 select the values that are in the domain of this function. Choices: − 5 − 1 1 Give the Domain f ( x ) = 4 √ 2 − 3 x + 7 x Give the Domain f ( x ) = x + 2 x − 3 Give the Domain f ( x ) = 2 x − 3 x 2 − 4 Give the Domain f ( x ) = 2 x − 3 x 2 + 4 4 Give the Domain f ( x ) = x + 1 x 2 − x − 6 Give the Domain f ( x ) = x + 1 x 2 + x − 1 Some eGrade problems just ask: Is the Domain “all reals” or “not all reals”? You can use the from the quadratic formula to answer. Domain “all reals”? f ( x ) = x + 1 x 2 + x − 1 Domain “all reals”? f ( x ) = x + 1 x 2 + x + 1 Domain “all reals”? f ( x ) = x − 3  x + 1  f ( x ) = x 5 − x − 3 x 2 5 Domain “all reals”? f ( x ) = 5 x 2 − x + 6 f ( x ) = x 3 + 2 x − 4 Domain “all reals”? f ( x ) = x + 1 3 √ x − 2 f ( x ) = x + 1 √ x − 2 —————————————————————————————————————– Obj 10d Find information from and about the graph of a function.Find information from and about the graph of a function....
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This document was uploaded on 11/01/2011 for the course MAC 1105 at FSU.
 Fall '08
 EVERAGE
 Algebra, Sets

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