Function Notation and Linear Functions Section 2.2 Function Notation and Linear Functions

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

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

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

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

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

4. Use the function and your calculator to complete the table below.

5. Use the function and the Graph-Table feature on your calculator to complete the table below. (See Calculator Perspective 2.2.2.)

6. The graph shown below defines a function that has an algebraic form Use this graph to determine the requested input and output values. (a) ______ Graph (If the input value is 0, what is the output value?) (b) ______ (c) for ______ (What is the input value if the output value is 0?) (d) for ______

7. The table shown below defines a function that has an algebraic form Use this table to determine the requested input and output values. (a) ______ Table (If the input value is 2, what is the output value?) (b) ______ (c) for ______ (What is the input value if the output value is 2?) (d) for ______

8. Comparing the Graphs of an Arithmetic Sequence and a Linear Function Graph of an Arithmetic Sequence Graph the first five terms of the sequence defined by Graph of a Linear Function Graph the linear function by plotting the points with x-coordinates of 1, 2, 3, 4, and 5, and then sketch the line through these points. .

Objective: Write a function to model an application. 9. 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 xth month. __________________ (b) Give the total paid by the end of the 36th month. __________________

10. 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. Amount of first investment Amount of second investment 1,000 1,500 2,300

11. 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. Length of first piece Length of second piece 1 7 8

12. You have 40 feet of fencing to enclose three sides of a rectangular pen, and x represents the width of the pen. Write a function that represents the length of the pen. Then complete the table of values. Width Length 5 10 15 wall x

13. 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 water Total volume 5 8 12

14. The price of every item in a store has been marked down by 10% 14. 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. (c) Complete the following table for the new price of each item whose original price is given. Original price New price 22 45 80

15. 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. (d) Evaluate the function in part (c) using .