1. Unit 7 - Functions
Learning Target : I can determine if a relation is a function. A "relation" is just a relationship between sets of information. A function is a relationship that assigns exactly one output value to one input value.

2. Unit 7 - Functions
Now if we change the number line to people on the x-axis it becomes a function. Everyone has only one birthday.
Everyone place your birthday on a number line that lists the days of the year as the x value This is not a function since many days have multiple birthdays

3. Functions can also be shown as graphs
The vertical line test can be used to show if a relation is a function

4. Vocabulary you should know
Function - This is like an equation, one output per one input
Domain – Input Value, or x-values
Range - Output Value, or y-values
Function Table - Organizes the information

5. Determine if ordered pairs are a function
(1, 1) (2, 2) (3, 3) Function (1, 1) (2, 1) (3, 3) (1, 1) (1, 2) (3, 3) Not a Function

6. Determine if a mapping of points are a function.1 5 7 3 2 4

7. Determine if a mapping of points are a function.1 5 7 3 2 4

8. Determine if a graph is a function

9. Determine if a graph is a function

10. LT: I can represent linear functions
Define Linear A line contains at least two points
Define Linear Function Line that is a function. There is one line that is not a function, can you name it? Vertical Line

11. Day 2. Read Page 469 -470. Can you complete the following function table?
Given the function f(x) = x + 5 Domain { -2, -1, 0, 1, 2} Range { 3, 4, 5, 6, 7}

12. Do You know where the domain, function, and range go in the function table?
Domain or x
Function
f(x) = x + 5
Range or f(x) -2
-2 + 5 3
Domain or x
Function
f(x) = x + 5
Range or f(x) -2
-2 + 5 3 -1
-1 + 5 4
0 + 5 5 1
1 + 5 6 2
2+ 5 7

13. Can you complete a function table given the function and domain?
Given the function f(x) = 2x + 3
Domain { -2, -1, 0 1, 2}
This time you must find the range
How much do you know?
Domain or x
Function
f(x) = 2x + 3
Range or f(x) -2 -1 1 2

14. Table filled in -2 2(-2) + 3 -1 2(-1) + 3 1 2(0) + 3 3 2(1) + 3 5 2
Domain or x
Function
f(x) = 2x + 3
Range or f(x) -2
2(-2) + 3 -1
2(-1) + 3 1
2(0) + 3 3
2(1) + 3 5 2
2(2) + 3 7

15. Unit 7.2 Graphing Functions
Recall how to graph an ordered pair (x, y)
The x value is left or right, y up or down

16. Write down the following
Mr. Scott’s Graphing helpful hints
1) f(x) and y are the same values on a graph
If a domain is not given use { -2, -1, 0, 1, 2}
If there is a fraction with the x, use multiplies of the denominator for your domain.
You may have to change the y- axis value so you can put a few ordered pairs on your graph

17. Example 1 Graph y = 3x + 5 -2 3(-2) + 5 -1 3(-1) + 5 2 3(0) + 5 5 1
Make a table
Completed Table x
y = 3x + 5 y -2
3(-2) + 5 -1
3(-1) + 5 2
3(0) + 5 5 1
3(1) + 5 8
3(2) + 5 11 x
y = 3x + 5 y -2 -1 1 2

18. Write as ordered pairs and graph
(-2, -1)
(-1, 2)
(0, 5)
(1, 8)
(2, 11)

19. Example 2 y = x + 1
Make a table with multiplies of 3 and 0 x
y = 𝟐 𝟑 x + 1 y -6 -3 3 6

20. Example 2 y = 2 3 x + 1 Completed Table Graph the ordered pairs -6
𝟐 𝟑 (−6) + 1 -3
𝟐 𝟑 (−3) + 1 -1
𝟐 𝟑 (0) + 1 1 3
𝟐 𝟑 (3) + 1 6
𝟐 𝟑 (6) + 1 5
Completed Table
Graph the ordered pairs

21. Read Page 198 - 199 3 things to consider
With your group Read and Answer the Check Your Progress Questions and Check them with me. There is an a, b, and c. You can use a calculator.
Change in value = present value – previous value ( moving backwards)
Rate of Change = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑎𝑙𝑢𝑒𝑠 𝑡𝑖𝑚𝑒 (𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒)
3 things to consider
Unit Rate should have a denominator of 1
Positive or Negative
Label both

22. Unit 7 LT 3: Find the rate of change given a graph or table
Rate of Change is a rate the describes how one quantity changes in relation to another Table can be vertical = time is left column
Given the table find the rate of change between days 2 and 6?
240 −80 6 −2 = = 40 𝑚𝑖𝑙𝑒𝑠 1 ℎ𝑜𝑢𝑟

23. Tables
Find the rate of change between rides 2 and − −2 = = $ 𝑟𝑖𝑑𝑒 Find the rate of change for days 2 and − −2 = −$ 𝑑𝑎𝑦

24. Rate of Change for a graph = Δ𝑦 Δ𝑥

25. Quick Quiz x Y 1 9 2 8 3 7 4 6 5 x f(x) = 3x f(x) -2 2 56 2 126 3 176
Function or Not? 2. Fill out the table 3. Find the rate of
change between 3 and 5 x Y 1 9 2 8 3 7 4 6 5 x
f(x) = 3x
f(x) -2 2
Hours
Distance in miles 56 2
126 3
176 5
276

26. 7.3 LT: I can find a constant rate of change
Define Constant Linear Functioins have a Constant Rate of Change

27. Check for understanding
Does the following have a constant rate of change?
Does the following graph have a constant rate of change?

28. Proportional Relationships – Page 206

29. Proportional Relationships – Page 206
Example of one that is not
Example that is, all ratios are = .45

30. Everyday use of slope – Handicap accessible
The least possible slope shall be used for any ramp. The maximum slope of a ramp in new construction shall be 1:12. The maximum rise for any ramp run shall be 30 inches. (American Disabilities Act) Which means for every foot of rise, you need 12 feet of length.

32. 7. 4 LT I can find the slope between two points
7.4 LT I can find the slope between two points. Slope – steepness of a line

33. 7.4
A lowercase m is used to abbreviate slope Slope = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 Scott’s Slope Definition m = 𝑢𝑝 𝑜𝑟 𝑑𝑜𝑤𝑛 𝑙𝑒𝑓𝑡 𝑡𝑜 𝑟𝑖𝑔ℎ𝑡
Given the points (1,1) and (6,3) on a coordinate plane. Can you find the slope? Is it positive or negative?

34. 7.4 Another example

35. Put in notes - Correct way to find slopes

36. Examples – remember left to right

37. Two Special Slopes

38. Page – 22, be careful on 2 and 3
Just by looking, what is the slope ?
I feel this is an incorrect way to find slope, Why?

39. Slope – Day 2 Find the slope between two points
( 𝑥 1 , 𝑦 1 ) ( 𝑥 2 , 𝑦 2 ) (2, 4) (5, 13) Place numbers in formula 13 −4 5 −2 9 3 = 3

40. ( 𝑥 1 , 𝑦 1 ) ( 𝑥 2 , 𝑦 2 ) ( -5, 0) and (-2, -4) −4 −0 −2−(−5) −4 3
( 𝑥 1 , 𝑦 1 ) ( 𝑥 2 , 𝑦 2 ) (-3, 5) and (-3, 2) 2 −5 −3−(−3) −3 0 Undefined Slope

41. Slopes – Day 3
Bell Ringer - In your notebook, please complete the following. From your notes on slope; write down at least two ideas about slope in complete sentences, with correct capitalization and spelling. ( 4 minutes )

42. Example of writing
Slope measures the steepness of a line. The slope of a line can be negative, positive, zero, or undefined. The slope formula is the rise of line divided by the run of the line. Slope is always measured from the left point to the right point.

43. Expanding Slopes to Tables
Remember how rate of change was found.
Rate of change = 67 −55 5 −1 = =
3 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 1 𝑑𝑎𝑦𝑠
It is the same for slope. You will do the same thing except it will be for an x and y table
Slope between 1 and 2 = 4−(−5) 2−1 = 9
Date 1 5 8
Temp 55 67 52 x 1 2 3 y -5 4 7

44. Quick Quiz
What is the rate of change between A and B B and C C and F 5 𝑚𝑝ℎ 1 𝑠𝑒𝑐 0 𝑚𝑝ℎ 1 𝑠𝑒𝑐 −2 𝑚𝑝ℎ 1 𝑠𝑒𝑐