a Table of Ordered Pairs Domain Domain Range Range Function Function b Set of

# A table of ordered pairs domain domain range range

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a) Table of Ordered Pairs Domain: Domain: Range: Range: Function: Function: b) Set of Ordered Pairs Domain: Range: Function: Domain: Range: Function: ( ) ( ) ( ) ( ) { } 0,1 , 1,3 , 3,0 , 5,3 ( ) ( ) ( ) ( ) { } 2,1 , 1,3 , 0, 5 , 1,0
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 15 Example 2: For the following graphs find the Domain/Range in interval notation; then state whether it is a function or not. a) 𝑦𝑦 = 2 𝑥𝑥 + 8 b) 𝑦𝑦 = 𝑥𝑥 2 + 4 c) 𝑥𝑥 = 𝑦𝑦 2 domain: ________________ domain: ________________ domain: _____________ range: __________________ range: __________________ range: ______________ function: ___________________ function: ___________________ function: _______________ d) 𝑦𝑦 = | 𝑥𝑥 | 1 e) 𝑥𝑥 = 7 f) 𝑦𝑦 = 4 domain: ________________ domain: ________________ domain: _____________ range: __________________ range: __________________ range: ______________ function: ___________________ function: ___________________ function: _______________ Vertical Line Test Rule: If a vertical line crosses the graph of a relation in more than one place, the relation ______________________________________________________.
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 16 S ECTION 2.3: F UNCTION N OTATION Function Notation: 𝑢𝑢 ( 𝑥𝑥 ) 𝑢𝑢 is the function name while 𝑥𝑥 is the input and 𝑢𝑢 ( 𝑥𝑥 ) is the output. The function 𝑦𝑦 = 2 𝑥𝑥 + 1 is the same as___________________________. Example 1: Solve the following a) Given: 𝑦𝑦 = 2 𝑥𝑥 + 1 Given: 𝑢𝑢 ( 𝑥𝑥 ) = 2 𝑥𝑥 + 1 Find 𝑦𝑦 when 𝑥𝑥 = 6 Find 𝑢𝑢 (6) Example 2: Find the function values for each: a) 𝑢𝑢 ( 2) 𝑖𝑖𝑢𝑢 𝑢𝑢 ( 𝑥𝑥 ) = 3 𝑥𝑥 2 2 𝑥𝑥 + 8 b) 𝑢𝑢 (2 𝑦𝑦 ) 𝑖𝑖𝑢𝑢 𝑢𝑢 ( 𝑥𝑥 ) = 3 𝑥𝑥 2 2 𝑥𝑥 + 8 c) 𝑟𝑟 (20) 𝑖𝑖𝑢𝑢 𝑟𝑟 ( 𝑥𝑥 ) = √𝑥𝑥 + 5 d) 𝑟𝑟 (2 𝑥𝑥 − 1) 𝑖𝑖𝑢𝑢 𝑟𝑟 ( 𝑥𝑥 ) = √𝑥𝑥 + 5 e) 𝑢𝑢 �− 2 3 𝑖𝑖𝑢𝑢 𝑢𝑢 ( 𝑥𝑥 ) = 18 𝑥𝑥 3 + 𝑥𝑥 2 3 𝑥𝑥 + 12
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 17 Example 3: If the function f is given by 𝑢𝑢 = {( 2,0), (3, 1), (2,4), (7,5)}, find 𝑢𝑢 ( 2), 𝑢𝑢 (3), 𝑢𝑢 (2), 𝑎𝑎𝑖𝑖𝑢𝑢 𝑢𝑢 (7). Example 4: For the following graphs find the values of the functions. a) 𝑢𝑢 (1) = __________ 𝑢𝑢 ( 2) = ____________ b) 𝑢𝑢 (0) = __________ 𝑢𝑢 (1) = __________
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 18 S ECTION 2.4: A LGEBRA AND C OMPOSITION WITH F UNCTIONS If we are given two functions, f and g , with a common domain, then we can define four other functions as follows: Example 1: If 𝑢𝑢 ( 𝑥𝑥 ) = 4 𝑥𝑥 − 3 and 𝑟𝑟 ( 𝑥𝑥 ) = 4 𝑥𝑥 2 7 𝑥𝑥 + 3 a) Find ( 𝑢𝑢 + 𝑟𝑟 )( 𝑥𝑥 ) ; evaluate ( 𝑢𝑢 + 𝑟𝑟 )(2) b) Find ( 𝑢𝑢𝑟𝑟 )( 𝑥𝑥 ) ; evaluate ( 𝑢𝑢𝑟𝑟 )(0) c) Find ( 𝑟𝑟 − 𝑢𝑢 )( 𝑥𝑥 ) ; evaluate ( 𝑟𝑟 − 𝑢𝑢 )( 1)
MTH 111 College Algebra CHAPTER 2 NOTES Kelkenberg 19 In addition to the four operations used to combine functions shown so far, there is a fifth way to combine two (or more) functions to obtain a new function. It is called the ______________________________________. To find the composition of two functions, 𝑢𝑢 and 𝑟𝑟 , we first require that the range of 𝑟𝑟 has numbers in common with the domain of 𝑢𝑢 . Then we write: This means we begin with a number, 𝑥𝑥 , and we operate on it with 𝑟𝑟 , giving us the value 𝑟𝑟 ( 𝑥𝑥 ) . Then we take the value 𝑟𝑟 ( 𝑥𝑥 ) and operate on it with 𝑢𝑢 , giving us 𝑢𝑢 ( 𝑟𝑟 ( 𝑥𝑥 )) .

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