1. Function Notation and Linear Functions
Section 2.2
Function Notation and Linear Functions

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

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

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

5. 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

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 your calculator to
complete the table below.

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

9. 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
______

10. 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
______

11. 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. .

12. 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. __________________

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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 .