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Lesson 5-2

Domain and Range

+Vocabulary

Domain: the set of all inputs for a function

Range: Set of all outputs for a function

Example: With the DVD problem discussed Monday, the domain would be {A1, A2, A3, B1, B2, B3, C1, C2, C3} and the range would be {The Hunger Sports, The Revengers, The Amazing Insectman, The Light Knight, The Dependables|

+Example

#1)Consider a vending machine where inserting 25 cents dispenses one pencil, inserting 50 cents dispenses 2 pencils, and so forth up to and including all 10 pencils in the vending machine.

A) What is the domain?

B} What is the range?

+Table Example

#2 a) Identify domain and range

+Mapping Example

#2 b) Identify domain and range

+Graphing Example

#2 b) Identify domain and range

+Ordered Pair Example

#2 d) Identify domain and range

{(-7, 0)}, {9, -3), (-6, 2.5)}

+Vending Machine

#3) Consider a machine that exchanges quarters for dollar bills. Inserting one dollar bill returns four quarters and you may insert up to five one dollar bills at a time.

A) Is 7 a possible input for the relation this change machine represents? Justify your response.

B) Could 3.5 be included in the domain of this relation? Explain why or why not.

C) What values are not in the domain? Justify your reasoning.

+Vending machine cont.

D) Is 8 a possible output for the relation this change machine represents? Justify your response.

E) Could 3 be included in the range of this relation? Explain why or why not.

F) What values are not in the range? Explain your reasoning?

+#4) Each of the functions that you have seen has a finite number of ordered pairs. There are functions that have an infinite number of ordered pairs. Describe any difficulties that may exist trying to represent a function with an infinite number of ordered pairs using the four representations of functions that have been described thus far.

+“Function Machine”

Sometimes machine diagrams are used to represent functions. In the function machine below, the inputs are labeled x and the outputs are labeled y. The function is represented by the expression 2x+5.

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#5a) What are the output if the input if the input is x = 7? x = –2? x = 1/3?

#5b) Is there any limit to the number of input values that can be used with this expression? Explain?

+Another function Machine

#6a) x = -5

B) x = 3/5

C) x = 10

+A couple more examples

Find the output values for each of the functions if the inputs are x = 0, x= -1, x= 4

A) y = 3x + 4

B) y = x2 – 1

C) y = 3(x – 4 ) + 12