Wednesday 9/24/14Bell Work

1.) Think of a correlation that occurred in the movie “Up.” The more ________, the more/less________.

2.) What is the difference between the two graphs? Explain. Graph 1

Graph 2

Learning Objective:

SWBAT Determine a function from a graph, table, and set of points.

Lesson 2.2: Determining a function

Recall:

A function is a rule in which for every _______, there is exactly ONE _______.

Recall:

A function is a rule in which for every _______, there is exactly ONE _______.

What does that look like?

Method YES, It’s a Function! No, it’s not a function: each value of x has MORE than one value for y.

1.) A Set of Points

(2, 100), (0.5, 50) (-2, -100), (4, 200)

(-2, 25) (4, 100)

(-2, -50) (1, 25) (0,0)

For one value of x, there are TWO values of y.

Method YES, It’s a Function!For each value of x, there is exactly one value of y.

No, it’s not a function: each value of x has MORE than one value for y.

2.) A table x y

3 9

9 12

10 13

80 83

x y

3 9

9 12

3 13

80 83

Method YES, It’s a Function! No, it’s not a function: each value of x has MORE than one value for y.

3.) A Graph

Definition:

Vertical Line Test: If a vertical line on the graph passes through more than one point, it is NOT a function.

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

EXAMPLE 1: Is the following a function? Explain. (-2, -5) (0,0) (2, 5) (1, 2.5)

Input Output

Answer: This _________( is/is not) a function. For every ______________, there _________ is/is not exactly one _______________________.

I. Points:

II. Graph:

III. Table

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

EXAMPLE 2: Is the following a function? Explain. (-3, 1) ( 0 , 3 ) ( 4, 3.5 ) (0, -1) (4,

-3.5)

This _________( is/is not) a function. For every ______________, there _________ is/is not exactly one _______________________.

I. Points:

II. Graph: Circle the part of

the graph that shows that there

are TWO values of y for one x.

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

EXAMPLE 3: Is the following a function? Explain. (-5, -2) (1, -2) (6, -2) (1, -2)

Input Output

This _________( is/is not) a function. For every ______________, there _________ is/is not exactly one _______________________.

I. Points:

II. Graph:

III. Table

Does it pass the vertical line test? Is there exactly one y for each x? Are there more than two values of y for x?

Practice:Determine which one of these is NOT a function. Explain your reasoning.

AB.

• For every value of x, there is only ONE value of y.• Does it pass the vertical line test? • Give your answer.

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

x y

4 26

5 32

11 24

9 20

8 18

(0,0) (1,2) (2,4) (3,6) (4,8)

Input Output

0 20

1 4

9 24

9 20

8 18

x y

1 1

-4 16

8 64

2 4

4 16

Bell Work 9/25 Which of the following graphs represents a function ?

Justify your answer.

“Graph __________ is a function because__________”

Thursday 9/25/14Bell Work

1. Is the graph below a function? Use the vertical line test.

2. Write down four points from the graph above.

3. “For every x, there is one unique y.” Does the opposite apply— “For every y, there is exactly one x”? Use the examples above to justify your answer.

1 2 3 4 5 6–1–2–3–4–5–6 x

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

y

Friday 9/26/14Bell Work

1. Explain what you would do to determine whether this table represents a function:

2. Give me one math concept that you learned these past six weeks. NOT A TOPIC! A fact or statement.

Input Output-2 70 18-2 7

4 12

Friday 9/26/14Bell Work

1. Explain what you would do to determine whether these points represent a function:

(4, 8) (9,12) (4, 8) (7, 12) (0, 12)

2. Give me one math concept that you learned these past six weeks. NOT A TOPIC! A fact or statement. And one thing you look forward to this next week!