What is a function
-
Upload
julienorman80065 -
Category
Education
-
view
173 -
download
0
Transcript of What is a function
![Page 1: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/1.jpg)
HousekeepingLast week: • Unit 1 Pretest – Functions• MAP tests
![Page 2: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/2.jpg)
Unit 1 FunctionsUnit Summary: In this unit, students will be introduced to the concept of functions. Emphasis will be placed on the definition of function, domain and range, evaluating functions, calculating slope of a linear function, identifying the rate of change of a function and whether it is increasing or decreasing, and representing functions in different ways.
![Page 3: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/3.jpg)
![Page 4: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/4.jpg)
Learning Objectives: Upon successful completion of this unit, students will be able to:• define function• recognize a function and determine its domain and range• evaluate a function using substitution• calculate slope and compare rates of change for linear
functions• construct an equation from a graph or table of values• model real world situations with functions
![Page 5: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/5.jpg)
Essential Questions/What is the Purpose for Learning This?
Make sure you can answer these questions before attempting the Unit Test.
Why are relations and functions represented in multiple ways?
How are properties of functions and functional operations useful?
![Page 6: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/6.jpg)
Lesson ContentLesson 1: Defining Functions--learn the definition of a function; determine the domain and range; recognize when an equation is not a functionLesson 2: Evaluating Functions--use substitution to evaluate a function; realize that for a function, every input has only one outputLesson 3: Comparing Functions--calculate slope; compare the rate of change for various equations; represent functions in multiple waysLesson 4: Using Functions to Model Linear Relationships--interpret the rate of change from a model; identify if a function is increasing or decreasing; construct and equation with information from a graph or table
![Page 7: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/7.jpg)
Lesson 1: Defining a Function
• learn the definition of a function• determine the domain and range• recognize when an equation is not a function
![Page 8: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/8.jpg)
Why are functions important to me if I’m buying candy at the local store?
![Page 9: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/9.jpg)
![Page 10: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/10.jpg)
![Page 11: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/11.jpg)
In this lesson you will learn what a function is by
evaluating examples of relations.
![Page 12: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/12.jpg)
A relation is any pairing of numbers.
Candy Bars to Price
Paul: (2 bars, $1.50)You: (2 bars, $3.50)
![Page 13: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/13.jpg)
Candy Palace
(2 bars, $1.50)(2 bars, $3.50)(3 bars, $5.00)
Sweet Factory
(1 bars, $0.75)(2 bars, $1.50)(3 bars, $2.25)
Two Kinds of Relations
No RuleRule
![Page 14: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/14.jpg)
A FUNCTION is a special type of relation in which a rule assigns every input exactly one
output.
4321
Inputs
12963
Outputs
Function
![Page 15: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/15.jpg)
A Common MistakeInput (x) Output (y) Output (y)Input (x)
1 2 3 4
3 6 9 12
1 2 3 4
3 6 9 12Function! Not a function!
![Page 16: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/16.jpg)
A FUNCTION is a special type of relation in which a rule assigns every input exactly one
output.
Bars Price
1 $0.75
2 $1.50
3 $2.25
4 $3.00Function
Candy Bars to Price
Paul: (2 bars, $1.50)You: (2 bars, $3.50)
Not a
Function
![Page 17: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/17.jpg)
Weeks Books
1 2
2 4
3 6
4 8
… …
Reading Two Books / Week
Is the Relation a Function???
![Page 18: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/18.jpg)
Hours Problems Correct1 341 652 422 323 534 67
Multiplication Facts
MayCoryBarb
SusanSilasLisa
If I tell you the input, can you
predict the output?
Is the Relation a Function???
![Page 19: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/19.jpg)
Input Output
1 3
2 6
3 9
4 12
Input Output
1 1
2 4
3 9
4 16
Input times 3 Input squared
Is the Relation a Function???
![Page 20: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/20.jpg)
How do you figure out if a gumball machine models a
function relation?
![Page 21: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/21.jpg)
Gumball Machine ExampleInput (x) Output (y)
![Page 22: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/22.jpg)
Gumball Machine ExampleInput (x) Output (y)
123
246
![Page 23: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/23.jpg)
Gumball Machine ExampleInput (x) Output (y)
123
462
![Page 24: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/24.jpg)
Another Gumball Machine Example
Input (x) Output (y)
![Page 25: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/25.jpg)
Another Gumball Machine ExampleInput (x) Output (y)
112
234
![Page 26: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/26.jpg)
Another Gumball Machine ExampleInput (x) Output (y)
1
2
234
![Page 27: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/27.jpg)
A FUNCTION is a special type of relation in which a rule assigns every input exactly one output.
![Page 28: What is a function](https://reader031.fdocuments.us/reader031/viewer/2022030212/58a0169b1a28ab9c418b5b8b/html5/thumbnails/28.jpg)