1. Section 2.2 Function Notation and Linear Functions

2. 2.2 Lecture Guide: Function Notation and Linear Functions Objective 1: Use function notation.

3. Function Notation: The notation is referred to as function notation and is is the ____________ valueread “______ of ______” or “ for an ____________ value of x.”

4. 1. (a) (b) Given, evaluate each of the following: (d) (c)

5. Objective 2: Use a linear equation to form a table of values and to graph a linear equation. 2.Use the function the following table and graph. Table Graph to complete

6. 3. The function from problem 2 is called a linear function because its graph is a __________________ __________________. Functions in the form are called linear functions.

7. 4. Use the function and a spreadsheet or a calculator to complete the table below. xf(x) 33 –2 –1 0 1 2 3

8. 5. Use the function x f(x) 0 10 20 30 40 50 60 calculator to complete the table below. and a spreadsheet or a

9. . Objective 3: Write a linear function to model an application. 6. Consider a car loan with payments of $200 per month and a down payment of $700. (a) Give a function that models the total paid by the end of the x th month. f(x) = _________________ (b) Give the total paid by the end of the 36 th month.

10. Amount of first investment Amount of second investment 1,000 1,500 2,300 7. If you make two investments totaling $3,000 and x represents the amount of one investment, write a function that represents the amount in the other investment. Then complete the table of values.

11. Length of first piece Length of second piece 1 7 8 8. If you have a 10-foot board that is to be cut in two pieces, and x represents the length of one of the pieces, write a function that represents the length of the other piece. Then complete the table of values.

12. 9. You have 40 feet of fencing to enclose three sides of a rectangular pen, and x represents the amount of fencing used for the width of the pen. Write a function that represents the amount of fencing remaining for the length of the pen. Then complete the table of values. wall Length of first piece Length of second piece 5 10 15

13. 10. An airplane has a speed of x mi/h in calm skies. (a) Write a function in terms of x for the rate of this airplane traveling in the same direction as a 20-mi/h wind. (b) Write a function in terms of x for the rate of this airplane traveling in the opposite direction of a 20-mi/h wind. (c) Write a function in terms of x for the distance the airplane travels in 3 hours going in the same direction as a 20-mi/h wind.

14. 11. If you have a 2 gallons of insecticide to which you are planning to add some water to dilute the mixture. Letting x represent the number of gallons of water that you add, write a function that represents the total volume in gallons of the mixture. Then complete the table of values. Gallons of waterTotal volume 5 8 12

15. 12. The price of every item in a store has been marked down by 10%. Let x represent the original price of an item. (a) Write a function for the amount of discount on an item with an original price of x dollars. (b) Write a function for the new price of an item with an original price of x dollars.

16. Original priceNew price 22 45 80 (c) Complete the following table for the new price of each item whose original price is given. 12. The price of every item in a store has been marked down by 10%. Let x represent the original price of an item.

17. Graph Table 13. Use the given graph to complete the table.

18. 14. Use this table to determine the requested input and output values. Table (a) (If the input value is 2, what is the output value?) ______ (b) (c) (d) ______ for ______ (What is the input value if the output value is 2?) for ______

19. (a) ______ (If the input value is 0, what is the output value?) (b) ______ (c) for x = ______ (What is the input value if the output value is 0?) (d) for x = ______ 15. Use the given graph to determine the missing input and output values. Graph