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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. Were 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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 Fall '08
 EVERAGE
 Algebra, Sets

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