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Function Notation: f x
f xThe notation is referred to as function notation and is
is the ____________ valueread “______ of ______” or “
for an ____________ value of x.”
Objective: Use a linear equation to form a table of values and to graph a linear equation.
2. Use the function 3 4f x x the following table and graph.
Table
2
1
0
1
2
x f x
Graph
-12
4
-5 5
y
x
to complete
3. The function 3 4f x x from problem 2 is called a linear
function because its graph is a __________________ __________________. Functions in the form f x mx b are called linear functions.
5. Use the function 1f x x and the Graph-Table feature
on your calculator to complete the table below. (See Calculator Perspective 2.2.2.)
2.3, 2.3, 1 by 3.1, 3.1, 1
6. The graph shown below defines a function that has an algebraic form f x mx b . Use this graph to determine the requested input and output values.
Graph
-2
8
-2 8
y
x
0f (a)(If the input value is 0, what is the output value?)
______
(b)
(c)
(d)
2f ______
0f x for x ______ (What is the input value if the output value is 0?)
for x ______ 2f x
7. The table shown below defines a function that has an algebraic form f x mx b . Use this table to determine the requested input and output values.
Table 2f (a)
(If the input value is 2, what is the output value?)
______
(b)
(c)
(d)
4f ______
2f x for x ______ (What is the input value if the output value is 2?)
for x ______ 4f x
1 2
0 0
1 2
2 4
3 6
4 8
x f x
-5
5
-1 6
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
2 5na n .
Graph of a Linear FunctionGraph the linear function
2 5f x x by plotting thepoints with x-coordinates of 1, 2, 3, 4, and 5, and then sketch the line through these points.
na
n
-5
5
-1 6
y
x
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.
f x __________________
(b) Give the total paid by the end of the 36th month. __________________
Objective: Write a function to model an application.
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
x ____________f x
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
x ____________f x
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
x ____________f x
wall
xx
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
x ____________f x
14. The price of every item in a store has been marked down by 10%. Let x represent the original price of an item.
Original price New price
22
45
80
x ____________f x
(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.
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 230x .