Algebra 1 NotesName______
Lesson5.1Represent Functions as Ordered Pairs and Rules
After today’s lesson, you should be able to determine whether a set of ordered pairs is a function and identify the domain and range of a relation.(CA Algebra 16.0, 17.0, 18.0)
A relation is a ______of the elements of one set, called the ______, with the elements of another set, called the ______.
A relation can be represented by a set of ______.
The domain is the set of all ______
The range is the set of all ______
Examples: Identify the domain and range of each relation.
x / –4 / –1 / 2 / 3y / 1 / –5 / 8 / 1
1. 2. 3. You Try:
A relation is a function if for each ______element there is exactly ______range element.
Examples: Determine whether the relation is a function. Explain.
x / –1 / 0 / 3 / 3y / –2 / –3 / 0 / 1
x / 2 / 6 / 1 / –1
y / 1 / 3 / 8 / 3
4. 5.6.You Try:
Each domain element of a function is called an ______, and the corresponding range element is called an ______.
Function Rules
A function may be represented using a rule that relates one variable to another.
The input variable is called the ______variable.
The output variable is called the ______ variable because its value ______on the value of the input variable.
Examples: Write a rule for the function.
Algebra 1 Notes 5.1 – Page 1 N. Cavalieri
10/2/2018
7.
x / –1 / 0 / 1 / 4 / 9y / 2 / 3 / 4 / 7 / 12
Notice that each output (y value) is ______the corresponding input
(x value). The rule is ______.
x / –2 / 1 / 2 / 5 / 7y / –4 / 2 / 4 / 10 / 14
8.
Notice that each output
(y value) is ______the corresponding input
(x value).The rule is ______.
9. You Try:
x / 5 / 10 / 12 / 17 / 25y / 10 / 15 / 17 / 22 / 30
Algebra 1 Notes 5.1 – Page 1 N. Cavalieri
10/2/2018
10.Multiple Choice:Each output of a function is 6 more than the corresponding input. Which equation is a rule for the function?
A.B. C. D.
You can use a function rule with values of the domain to determine the range.
Examples: Make a table of ordered pairs that represents the function. Then identify the range of the function.
Algebra 1 Notes 5.1 – Page 1 N. Cavalieri
10/2/2018
11. Domain:
x y (x, y)
Range:
12.
Domain:
x y (x, y)
Range:
13.You Try:
Domain:
x y (x, y)
Range:
Algebra 1 Notes 5.1 – Page 1 N. Cavalieri
10/2/2018
14.Multiple Choice: The domain of the function is. Which number is in the range of the function?
A.B. 11C. 12D.17
Examples: Write a rule for each situation.
15. There are x pieces of candy in a bowl to give out on Halloween. 47 pieces are given out. Write a rule for the number y of pieces of candy left in the bowl as a function of x.
16. You Try: Pens are on sale for $1.49 each. Write a rule for the amount y you spend as a function of the number x of pens you buy.
17. At the video store, the DVD’s on the sale table are $10 each.
(a) For each DVD you buy, you spend $10, so the ______
is a function of the number of ______.
(b)Write a rule for the amount y you spend as a function of the number x of DVD’s you buy.
(c)You find 4 DVD’s you like. You are trying to decide how many of them to buy.
What is the domain for your function?
(d)Make a table that represents the set of ordered pairs for the function. Then identify the range of the function.
Algebra 1 Notes 5.1 – Page 1 N. Cavalieri
10/2/2018