relations and functions - mr. aceves...
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1st Nine Weeks Week 1.2
Relations and Functions2A.1A; OBJ 1: A.1D, OBJ 2: A.2B, OBJ 3: A.5A
I. Warm up
Use the graph for Problems 1–3.
1. Fill in the table to match the above graph.
x
y
2. List the x-coordinates of the points.
3. List the y-coordinates of the points.
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II. Lesson notes
What does the word relationship mean? In mathematics how is this definition applied?
A relation is: ________________________________________________________________
______________________________________________________________________________________________________________________________________________________
How are patterns relations? Do patterns have an input and output value?
The set of all ___________ is called the domain, and the set of all __________ is called the range.
There are many different ways that relations can be represented:
Mapping Diagram:
Set of Ordered Pairs:
Table:
Graph:
Verbal Description:
Example 1: What is the domain and range of the following relations?
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A. {(100,5), (120,5), (140,6), (160,6), (180,12)}.
B.
C. X 1 2 5 8
Y 6 7 9 5
D. Students and their test scores.
Try it: Give the domain and range for the relations:
A. {100, 5), (120, 5), (140, 6), (160, 6), (180, 12)}
B.
C.
Relations as Functions:
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Suppose you are told that a person entered a word into a text message using the numbers 6, 2, 8, and 4 on a cell phone. It would be difficult to determine the word without seeing it because each number can be used to enter three different letters.
However, if you are told to enter the word MATH into a text message, you can easily determine that you use the numbers 6, 2, 8, and 4, because each letter appears on only one numbered key.
A relation in which the first coordinate is never repeated is called a function.
A function is: _______________________________________________________________
______________________________________________________________________________________________________________________________________________________
Example 2: Determine whether each is a relation or a function.
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A. from the items in a store to their prices on a certain date
B. from types of fruits to their colors
C.
Try it: Determine whether each relation is a function.
A.
B. From car models to car colors.
C.
Vertical Line Test:
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Every point on a vertical line has the same x-coordinate, so a vertical line cannot represent a function. If a vertical line passes through more than one point on the graph of a relation, the relation must have more than one point with the same x-coordinate. Therefore,
Example 3: Using the vertical line-test determine if the relation is a function. If not, then identify two points where the relation fails the test.
A.
B.
Try it: Use the vertical line test to determine if the relation is a function.
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A.
B.
C.
NAME_____________________________________DATE____________________PER.____
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Independent Practice: Relations and functions
Give the domain and range for each relation.
1. {(0, -2), (0, 2), (3, -1), (3, 1), (4, 0)}
___________________________
___________________________
2.
____________________________
____________________________
3.
_____________________________
_____________________________
4.
____________________________
____________________________
Determine whether each relation is a function.
5.
_____________________________
6.
_____________________________
7. From the day of the week to the number of hours in that day.
_____________________________
8.
_____________________________
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Use the vertical line test to determine whether each relation is a function. If not, identify two points where the relation fails.
9.
10.
11.
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
NAME_____________________________________DATE____________________PER.____
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TAKS Practice: OBJ 1: A.1D, OBJ 2: A.2B, OBJ 3: A.5A
Choose the correct answer choice for each question.
1. Which relation is NOT a function?
a. {(0, 1), (1, 0), (2, 0), (3, 1)}
b. {(-1, 5), (-2, 4), (-2, 3), (-3, 2)}
c. {(1, 1), (2, 2), (3, 3), (4, 4)}
d.
2. Which set represents the domain of {(99, -2), (99, -3), (96, -4), (96, -5)}?
a. {96, 99}
b. All negative integers
c. {-2, -3, -4, -5}
d. {-2, -3, -4, -5, 96, 99}
3. Which is an element of the range of the graphed function:
a. -2
b. 0
c. 1
d. 4
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