1. Domain and Range Day 1 Revised ©2014, Viet.dang@humble.k12.tx.us
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Domain and Range

2. Definitions A relation is between two variables of x and y
An ordered pair consist of a x and y–coordinate in brackets
It may be viewed as ordered pairs, mapping design, table, equation, or written in sentences
X–values can be known as inputs, domain, independent variable
Y–values can be known as outputs, range, dependent variable
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Domain and Range

3. What is a Relation or a Function?
What is a function? Can a function be a relation? Can a relation be a function? NO REPEATING X-Coordinates
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Domain and Range

4. Function Machine
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Domain and Range

5. “A doctor needs his or her ID to eXamine you”
Definitions x y D R I
“A doctor needs his or her ID to eXamine you”
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Domain and Range

6. Example 1 Is this relation a function? 2/28/2019 8:59 PM
Domain and Range

7. Your Turn Is this relation a function? 2/28/2019 8:59 PM
Domain and Range

8. Boys vs Girls a b c 1 2 3 a b c 1 2 3 Is this relation a function?
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Domain and Range

9. Example 2 3 1 –1 2 Would this mapping be considered a function?–1 2
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Domain and Range

10. Your Turn Would this mapping be considered a function?
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Domain and Range

11. What do these signs mean?
>
Greater than ≥
Greater than OR equal to
<
Less than
Less than OR equal to ≤
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Domain and Range

12. Definitions
Inequality is an equation where the variable does not equal to each other
>, <, or ≠ requires the dot being OPEN hole
>, <, or = required the dot being CLOSED hole
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Domain and Range

13. To Write Inequalities
Simple Inequalities (only ONE starting or ending point)
Follow the arrow
Variable Should always go first
Compound Inequalities (more than ONE starting or ending point)
Always use < or < in between the variable
Smallest number ALWAYS comes first
Biggest number ALWAYS comes last
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Domain and Range

14. Example 3
What is the domain and range? Write them in Compound Inequality form, if it is a function.
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Domain and Range

15. Example 4
What is the domain and range? Write them in Compound Inequality form, if it is a function.
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Domain and Range

16. Example 5
What is the domain and range? Write them in Compound Inequality form.
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Domain and Range

17. Example 6
What is the domain and range? Write them in Compound Inequality form, if it is a function.
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18. Example 7 Identify the domain and range below. 2/28/2019 8:59 PM

19. Example 8 Identify the domain and range below. 2/28/2019 8:59 PM

20. Your Turn
What is the domain and range? Write them in Compound Inequality form.
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Domain and Range

21. Vertical Line Test
Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point.
NO REPEATING X-COORDINATES
“The Pencil Test”
Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function
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Domain and Range

22. Example 9 Would this graph be a function? 2/28/2019 8:59 PM
Domain and Range

23. Example 10 Would this graph be a function? 2/28/2019 8:59 PM
Domain and Range

24. Your Turn Would this graph be a function? 2/28/2019 8:59 PM
Domain and Range

25. Example 11
Given g(x) = x2 – 3, determine g(2).
(2)2
g(2) = 4 – 3
g(2) = 1
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26. Example 12 Given f(x) = x2 – 2x + 4, evaluate f(–5). 2/28/2019 8:59 PM
Domain and Range

27. Your Turn Given f(x) = x2 – 6x + 9, evaluate f(1/2). 2/28/2019 8:59 PM
Domain and Range

28. Assignment
Worksheet
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Domain and Range

29. Test Distribution 1st 2nd 6th 7th A 3 8 4 6 B 10 9 7 C 5 D 1 2 F
No-Shows
100+
Range
59-100
42-100
48-94
52-97
Avg
79.91
77.71
76.29
78.04
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Domain and Range