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CA_GPS_1

# CA_GPS_1 - 1 State whether each relation defines a function...

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Rev. S08 http://faculty.valenciacc.edu/ashaw/ COLLEGE ALGEBRA NAME: ________________________________ GPS # 1 1.1 FUNCTIONS AND MODELS Class Time: ____________ Date: __________ Useful Definitions: Let X and Y be two nonempty sets. * A relation is a set of ordered pairs. For example: {( 1,4),( 3,5),(1,2),(7, 2)} ! ! ! * A function is a relation in which, for each value of the first component of the ordered pairs, there is exactly one value of the second component. * A function from X into Y is a relation that associates with each element of X exactly one element of Y . * In a relation, the set of all values of the independent variable is the domain ; the set of all values of the dependent variable is the range . * Vertical Line Test: If every vertical line intersects the graph of a relation only once, the relation is a function
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Unformatted text preview: . 1. State whether each relation defines a function and give the domain and range . a) {( 1,4),( 3,5),(1,2),(7, 2)} ! ! ! b) {(2,7),(3, 4),(2,0),(1, 2)} ! ! 2. Use “vertical line test” to check whether each relation defines y as a function of x . Give the domain . a) 2 x y = b) 1 2 2 = + y x c) 2 y x = d) 3 y x = 3. Let ( ) 2 3 f x x = ! + and 2 1 ( ) 3 1 4 g x x x = ! + + . Find the following. a) (1) f = b) ( 2) g ! = c) ( ) f m = d) ( ) g x ! = e) ( 1) f x + = e) ( ) g k ! = f) ) ( ) ( x f h x f ! + = g) h x f h x f ) ( ) ( ! + = 4. Find the domain of each of the following functions: a) 5 ) ( 2 + = x x f b) 3 4 1 ) ( ! = x x g c) 9 2 ) ( 2 ! = t t t r b) u u h 2 10 ) ( ! =...
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