Topic : Linear Functions

1. Topic: Linear Functions Essential Question: What everyday relationships can we represent using graphs, tables and functions?Learning Goal(s)Students will be able to:□ Construct a function to model a linear relationship between two quantities□ Determine the rate of change and initial value of a linear function□ Interpret the rate of change and initial value of a linear function  Question(s)/Concepts NOTES & EXAMPLES You HAVE 8 MINUTES TO COMPLETE.TO DO NOW: 1) Use the given values to make a table of solutions: y = 2x – 1 when x = 1, 2, 3, 4 2) Begin filling out the “K” and “W” on your K-W-L once you finish task #1.

2. Correct Response for #1

3. Intro to Functions

4. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York If we can convince our principal, using functions, equations, graphs, and tables, that if we have certain fund-raisers, particularly a car wash, we may be able to take a trip to New York! So let’s talk business. We can prepare a presentation with CRAZY SWAG, so that the principal simply cannot refuse.  1st – Let us understand the LANGUAGE we need to use in the presentation. OK, so if we are going to have a car wash, our focus will be the money we are going to make from it.

5. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair Look at the table to determine a) How much are wecharging to wash each car? Is that the rate of change?b) What is the general rule or equation that we can use to figure out how much ANY # of cars washed cost?

6. Temperature Check

7. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair The number of cars washed and the money earned is what we call a RELATION. A RELATION is a set of ordered pairs. They have a special type of relation which is known as a FUNCTION. In a function, like this one, each input or DOMAIN VALUE is paired with EXACTLY ONE output or RANGE VALUE. What is the rate of change?

8. Temperature Check

9. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair Our Rule is:y = 3x Now that we know what the general rule is for determining the money earned for washing any number of cars, figure out how much would be earned for washing 4 cars?

10. Temperature Check

11. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair So we heard through the grape vine that a celebrity is considering sponsoring our trip. The celebrity decides to give us $1000 towards the trip. What will the new function rule be?

12. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair The new rule will be y = 3x + 1000. What does the $1,000 represent?

13. Temperature Check

14. Q’s & C’s NOTES & EXAMPLES Using Slopes and Intercepts 1000

15. Q’s & C’s NOTES & EXAMPLES Using Slopes and Intercepts Initial Value or Starting Point 1000

16. Question(s)/Concept(s) NOTES & EXAMPLES PROCESSING Our school in the City: New York, New York INPUT(Independentvariable) OUTPUT ($$S)(Dependent Variable) OrderedPair We need to construct a new table of values to graph the new function rule or equation y = 3x+1000. The x-values are already given in the table. Complete the table by determining the range values.

17. Temperature Check

18. Quick Checks 1) Use the table below to find the value of y when x = 5 2) Lorenzo needs to construct a table of values to graph the equation y = -2x + 1. The x-values are given below. Which of the following is the correct list of y-values for this table? A) 2, 3, 7, 1, 4B) -5, -3, 0, -1, -3C) -5, -3, 0, 1, 3D) 5, 3, 1, -1, -3

19. Quick Checks 3) Students are planning to see a movie. Since the students are going as a group, the students are eligible for a group rate for refreshments. The group will pay one fee of $30 upfront, so that every student may receive a snack and a drink. At the local movie theater it cost $12.00 for 2 students to see a movie. It costs $18 for 3 students, and it cost $24.00 for 4 students. a. What is the function rule that relates the number of students to the total cost the group would have to pay, when they go to the local movie theater? Describe what the variables represent. b. What is the initial value? c. What is the rate of change? What does the rate of change represent?

20. Trivia Question WORTH 5 EXTRA CREDIT POINTS Is it true that you have to go either up or down the y-axis first when graphing?

21. Exit Ticket • #1 – A group of students are planning a trip to a museum for an exhibit’s opening night. Because it is opening night, the group must pay one fee of $3, and a ticket must be purchased for each student. It costs $16.00 for 2 students’ tickets. It costs $24 for 3 tickets, and it cost $32.00 for 4 tickets. What is the function rule that relates the number of students to the total cost the group would have to pay to enter the exhibit? • A) f(x) = 3x + 8B) f(x) = 3xC) f(x) = 8x - 3D) f(x) = 8x + 3 • #2 – Use the table below to determine the value of y when x = 8 • A) 21 B) 2 C) 8 D) none of above • #3- A student needs to construct a table of values to graph the equation y = -3x + 2. Which of the following is the correct list of y-values for this table given the following x-values: 1, 2, 3, 4? • A)-1, -4, -7, -10 C) 1, 2, 3, 4 • B) 1, 4, 7, 10 D) 5, 8, 11, 14

22. Practice Makes Perfect Homework: The Independent Practice Problems

23. Independent Practice Answers

24. Retain for Mastery In your section titled, “Summary,” respond to the following questions, 1) How can we use functions to represent relationships?