1. Topic Two
Mrs. Daniel- Algebra 1

2. Table Contents: 3.1: Graphing Relationships
3.2: Understanding Relations & Functions
3.3: Modeling with Functions
3.4: Graphing Functions
4.1: Identify and Graphing Sequences
4.2 & 4.3: Construction and Modeling Arithmetic Sequences

3. Lesson 3.1: Graphing Relationships Essential Question: How can you describe a relationship given a graph and sketch a graph given a description?

4. Three hoses fill three different water barrels
Three hoses fill three different water barrels. A green hose fills a water barrel at a constant rate. A black hose is slowly open when filling the barrel. A blue hose is completely open at the beginning and then slowly closed. Match each hose with the appropriate graph below.

5. You and a friend are playing catch
You and a friend are playing catch. You throw three different balls to your friend. You throw the first ball in an arc and your friend catches it. You throw the second ball in a arc, but this time the ball gets stuck in a tree. You throw the third ball directly at your friend, but it lands in front of your friend, and rolls the rest of the way on the ground.

6. A bathtub is being filled with water
A bathtub is being filled with water. After 10 minutes, there are 75 quarts of water in the tub. Then someone accidentally pulls the drain plug while the water is still running, and the tub begins to empty. The tub loses 15 quarts in 5 minutes, and then someone plugs the drain and the tub fills for 6 more minutes, gaining another 45 quarts of water. After a 15-minute bath, the person gets out and pulls the drain plug. It takes 11 minutes for the tub to drain. This is a: discrete continuous graph. The domain is ___________ The range is __________

7. At the start of a snowstorm, it snowed two inches an hour for two hours, then slowed to one inch an hour for an additional hour before stopping. Three hours after the snow stopped, it began to melt at one-half an inch an hour for two hours.

9. Lesson 3.2: Understanding Relations and Functions Essential Question: How do you represent relations and functions?

10. Vocab: Relation
Relation: A visual representation of how inputs (x- values) and output (y-values) are related/connected.

11. Vocab: Function
Function: a special type of relation in which there is ONLY one output value for each input value. The “x- values” can not repeat.

12. Vocab: Domain & Range
Domain: all input/x-values Range: all output/y-values

14. Identify the domain & range? Is it a function?

15. Identify the domain & range? Is it a function?

16. Vertical Line Test
The vertical line test states that a relation is a function if and only if a vertical line does not pass through more than one point on the graph of a relation.

17. Function?

18. Function?

21. Lesson 3.3: Modeling with Functions
Essential Question: What is function notation and how can you use function notation to model real-world situations?

22. Vocab
Independent: Input value of the function. Dependent: The value of the dependent variable depends on, or is a function of, the value of the independent variable. Identify the dependent and independent variables: In the summer, as the temperature outside increases, the amount of electricity used increases.

23. Write an equation and identify the independent and dependent variables.
A lawyer’s fee is $180 per hour for his services. How much does the lawyer charge for 5 hours?
The admission fee at a carnival is $9. Each ride costs $1.75. How much does it cost to go to the carnival and then go on 12 rides?

24. Write a function in function notation for each situation
Write a function in function notation for each situation. Find a reasonable domain and range for each function. Manuel has already sold $20 worth of tickets and needs to sell some additional tickets at $2.50 per ticket. Write a function for the total amount collected from ticket sales. A telephone company charges $0.25 per minute for the first 5 minutes of a call plus a $0.45 connection fee per call. Write a function for the total cost in dollars of making a call.

25. Write a function in function notation for each situation
Write a function in function notation for each situation. Find a reasonable domain and range for each function. The temperature early in the morning is 17 C. The temperature increases by 2C for every hour for the next 5 hours. Write a function for the temperature in degrees Celsius.

26. Lesson 3.4: Graphing Functions Essential Question: How do you graph functions?

27. How to Graph a Function
Step 1: Select three to five x-values Step 2: Plug in x- values to equation and simplify to calculate y-values. Step 3: Plot ordered pairs. Step 4: Connect dots in smooth line or curve.

32. Graph: y = -x2 X
Work
Ordered Pair

33. Graph: y = -4x + 2 X
Work
Ordered Pair

34. Graph: y = x2 + 3 X
Work
Ordered Pair

35. The Mid-Atlantic Ridge separates the North and South American Plates from the Eurasian and African Plates. The function y = 2.5x relates the number of centimeters y the Mid-Atlantic Ridge spreads after x years. Graph the function and use the graph to estimate how many centimeters the Mid-Atlantic Ridge spreads in 4.5 years. X
Work
Ordered Pair

37. A cruise ship is currently 5 kilometers away from its port and is traveling away from the port at 15 kilometers per hour. The function y = 15x +5 relates the number of kilometers y the ship will be from its port x hours from now. How far will the cruise ship be from its port 2.5 hours from now?

38. Lesson 4.1: Identifying & Graphing Sequences Essential Question: What is a sequence and how are sequences and functions related?

39. Vocab
Sequence = a list of numbers in a specific order. Term = each element/number in a sequence. Explicit Rule = a way to specific term without finding the previous terms. Usually involves “plugging in”. Recursive Rule = defines a term by relating it to the value of a previous term.

40. Find the 1st Four Terms Using an Explicit Rule
Rule: 3n2 + 1

41. Find the nth Terms Using an Explicit Rule
Rule: n2 – 5; term 6 Rule: 4n - 3; term 11

42. Recursive Rule: Math: f(1) = 4 f(n) = f(n-1) + 10
Words: first term is 4
next term: add 10 to previous answer

43. Recursive Rule: Math: f(1) = 3 f(n) = f(n-1) + 5
Words: first term is _________
next term: add ___ to previous answer n
F(n)

44. Find the 1st 5 terms of the sequence
f(1) = 35 and f(n) = f(n - 1) – 2
f(1) = 45 and f(n) = f(n – 1) - 4

45. A pizza place is having a special
A pizza place is having a special. If you order a large pizza for a regular price of $17, you can order any number of additional pizzas for $8.50 each. Use the recursive rule f(1) = 17 and f(n) = f(n – 1) for each whole number n greater than 1. n
F(n)

46. A gym charges $100 as the membership fee and $20 monthly fee
A gym charges $100 as the membership fee and $20 monthly fee. Use the explicit rule f(n) = 20n to construct and graph the sequence. n
F(n)

47. Lesson 4.2 & 4.3: Constructing and Modeling Arithmetic Sequences Essential Question: What is an arithmetic sequence and how can you solve real-world problems using arithmetic sequences?

48. Vocab
Arithmetic Sequence = the difference between consecutive terms is always equal. ADD between terms Can be defined using explicit or recursive formula Common Difference = the difference between terms is abbreviated with “d”

49. Using the table…
The savings account begins with $2000 and $500 more is deposited each month. Explicit Rule : _______________________ Recursive Rule : ___________________

50. Using the table…
The table shows the number of plates left at a buffet after each hour. Explicit Rule : _______________________ Recursive Rule : ___________________

51. Write the Rule…
A. 100, 88, 76, 64, …. Explicit Rule : _______________________ Recursive Rule : ___________________ B. 0, 8, 16, 24, 32, …

54. Write an explicit rule…
The cost of a whitewater rafting trip depends on the number of passengers. The base fee is $50, the cost per passenger is $25.

56. Write an explicit rule…
The number of seats per row in an auditorium depends on which row it is. The first two has 6 seats, the second row has 9 seats, the third row has 12 seats, and so on.

57. Eric collects stamps. The graph shows the number of stamps that Eric has collected over time, in months. According to this pattern, how many stamps will Eric have collected in 10 months? Explicit Rule: ________________

59. The graph show the height, in inches, of a stack of boxes on a table as the number of boxes in the stack increases. Find the height of the stack with 7 boxes. Explicit Rule: _______________

60. The odometer on a car reads 34,240 on day 1
The odometer on a car reads 34,240 on day 1. Every day the car is driven 57 miles. If this pattern continues what will the odometer read on day 15? Explicit Rule: ____________________