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Bell Work 1/20/15
11. 3, 5 , 8
3y x
1x 1y
1 1y y m x x
22. 4, 7 , 1
3y x
1x 1y
Write in slope-intercept form the equation of the line passing through the given point and PERPENDICULAR to the given line.
1 1y y m x x
Yesterday’s Homework
1. Any questions?2. Please pass your homework to the front.
• Make sure the correct heading is on your paper.• Is your NAME on your paper?
• Make sure the homework is 100% complete.• Incomplete work will NOT be accepted.
Relations and Functions
04/19/23
Heading
TSWBAT: tell if a relation is a function or not.
Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.
4.2
Notes
• Relation= Any set of ordered pairs.
• EVERYTHING is a relation.• ALL ordered pairs and ALL lines.
• Function= A relation where for every input there is
exactly one output.
• Every function is a relation.
• Domain (the inputs)= all of the x-values of an ordered pair.
• Range (the outputs)= all of the y-values of an ordered pair.
NotesFunction or not?
Ex. Ex. Ex. Ex.
Function Not a Function
Not a Function
Function
Now you try.
D R D R D R D R
NotesExpress each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?
Ex.
3, 4 , 1, 2 , 2, 2 , 5, 1
3 41 22 25 1
3
1
2
5
4
2
2
1
3, 1, 2, 5 4, 2, 2, 1
NotesExpress each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?
Ex.
2, 3 , 0, 5 , 4, 3 , 5, 2
2 30 54 35 2
2
0
4
5
3
5
2
2, 0, 4, 5 3, 5, 2
Notes
Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?
Ex.
5, 2 , 3, 4 , 3, 1 , 4, 4
5 23 43 14 4
5
3
4
2
4
1
4
5, 3, 4 2, 4, 1, 4
Now you try.
Notes• Vertical Line Test
= A graph is a function if no vertical line touches more than one point.
Ex.Function or not?
Run a vertical line through the entire graph.
Do I ever hit the graph more than once?
Not a Function
Notes
Ex.
Function or not?
Function
Now you try.
Ex.
Function
Notes
Ex.
Function or not?
Not a Function
Now you try.
Ex.
Not a Function
Summary
Everything is a _______. A function is a relation that for every input there is only ____ output. With a graph, all you have to do is use the Vertical Line ____ to determine if something is a ________.
relationone
Testfunction
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Ticket Out the Door
Put your NAME on the paper.
When finished, turn your paper face DOWN.Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?
3, 5 , 3, 1 , 3, 2 , 3, 5
Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
Homework 4.2
Function or not? 4. 6.
Express each relation as a table, as a graph, and as a mapping diagram. What is the domain and range? Is it a function?
1. 2, 5 , 0, 3 , 2,4 , 5, 3
2. 4, 3 , 3, 1 , 3, 1 , 5, 2
3. 4, 2 , 2, 5 , 3,4 , 3, 2
5.