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Today’s Lesson:. What: Identifying a function Why : To identify a function and become familiar with basic function vocabulary. Input. Output. Coordinate plane review:. y. Q I. Q II. C. E. A. B. D. F. G. origin. x. Q III. Q IV. Essential vocabulary:. Ordered Pair

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Presentation Transcript
slide1

Today’s Lesson:

What:

Identifying a function

Why:

To identify a function and become familiar with basic function vocabulary.

Input

Output

slide2

Coordinate plane review:

y

Q I

Q II

C

E

A

B

D

F

G

origin

x

Q III

Q IV

slide3

Essential vocabulary:

Ordered Pair

A name we use for the x and _______ values that make up a point on the coordinate plane.

y

Relation

A group of ordered _____________________.

pairs

Function

A special ___________________ of relation where there is one and only one “y” value for every “x” value. (“x” can never repeat)

TYPE

All functions are relations, but

Not all relations are functions!!!

slide4

3 ways to name “X” and “Y”:

OUTPUT

DOMAIN

DEPENDENT

What is the Domain of the

following relation?

{(1,2); (2,3); (3, 4); (4,5)}

_____________________________________

D = {1, 2, 3, 4}

What is the Range of the

following relation?

{(1,3); (2,5); (3, 7); (4,9)}

______________________________________

R = {3, 5, 7, 9}

slide5

4 ways to represent a function:

As an equation

y = _______

4x - 2

With

___________

“y is equal to the product of 4 and x, minus two.”

WORDS

As a table

Recognize this pattern/ equation?

4

2

3

1

10

As a

_________

GRAPH

slide6

How to identify a function . . .

METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one _______ value that is the same #, then the relation is ___________ a function!

x

NOT

Are the following examples functions? Answer “YES” or “NO”

___________ 2) _____________ 3) ______________

YES

YES

NO

4) __________ { (-2, 0); (0, 2); (2, 0); (4, 6) }

YES

5) __________ { (-2, 0); (0, 3); (-2, 2 ); (5, 7) }

NO

slide7

METHOD TWO: VERTICAL LINE TEST—Look at the graph of the function. If any two points on the graph can be connected by a ________________ line, then the relation is NOT a function!

vertical

Are the following examples functions? Answer “YES” or “NO”

NO

YES

__________ 2) __________

3) __________ 4) __________

YES

NO

slide8

END OF LESSON

The next slides are student copies of the notes for this lesson. These notes were handed out in class and filled-in as the lesson progressed.

NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”) represent the homework assigned for that day.

slide9

NAME:

DATE: ______/_______/_______

Math-7 NOTES

What: identifying a function

Why: To identify a function and become familiar with basic function vocabulary.

Coordinate plane review:

Essential vocabulary:

Ordered Pair

A name we use for the x and _____ values that make up a point on the

coordinate plane.

Relation

A group of ordered __________________.

Function

A special _______________ of relation where there is one and only one “y” value for every “x” value. (“x” can never repeat)

All functions are relations, but

Not all relations are functions!!!

slide10

3 ways to name “X” and “Y”:

What is the Domain of the

following relation?

{(1,2); (2,3); (3, 4); (4,5)}

_________________________________

What is the Range of the

following relation?

{(1,3); (2,5); (3, 7); (4,9)}

_________________________________

4 ways to represent a function:

As an equation

y = _______

“y is equal to the product of 4 and x, minus two.”

With

___________

4

2

3

1

Recognize this equation??

As a table

As a _______

slide11

How to identify a function . . .

METHOD ONE: Look to see if the “x” values repeat . . . If there is more than one _______ value that is the same #, then the relation is ______ a function!

Are the following examples functions? Answer “YES” or “NO”

____________ 2) _______________ 3) _______________

4) __________ { (-2, 0); (0, 2); (2, 0); (4, 6) }

5) __________ { (-2, 0); (0, 3); (-2, 2 ); (5, 7) }

METHOD TWO: VERTICAL LINE TEST—Look at the graph of the function. If any two points on the graph can be connected by a ________________ line, then the relation is NOT a function!

Are the following examples functions? Answer “YES” or “NO”

1) __________ 2) __________ 3) __________ 4) __________

slide12

NAME:_________________________________________________________________________________ DATE:_____/_____/__________

Math-7 PRACTICE/ classwork

“ function vocabulary”

A __________________________________ is a group of ordered pairs. A ________________________________ is a special type of relation where all the “x” values match with one and only one “y” value. (the “x” can never repeat).

We have 3 ways to name both the “x” variable and the “y” variable. Fill in the missing information with the appropriate vocabulary:

What is the Domain of the following relation?

{(0,3); (-5,5); (-2, 7); (8,9)}

D = _________________________________

What is the Range of the following relation?

{(1,-2); (2,0); (3, 2); (4,4)}

R= _________________________________

6) What are the 4 ways to represent a function (from our notes)?

slide13

NAME:_________________________________________________________________________________ DATE:_____/_____/__________

Math-7 PRACTICE/ Homework

“ Is it a function??”

slide14

NAME:_________________________________________________________________________________ DATE:_____/_____/__________

Math-7 PRACTICE/ Homework

“ Identify a function from a graph”