Algebra Part 3
Guided Notes
Section 1.6- Represent Functions as Rules and Tables
A Function consists of:
▪ A set called the Domain, containing numbers called _______________(usually
the x’s)
▪ A set called the Range, containing numbers called _______________ (usually
the y’s)
▪ A pairing of inputs with outputs such that each input is paired with exactly one
output.
*The input variable may also be referred to as the ___________________
variable, and the output variable may be referred to as the
____________________ variable.
Input – output values may sometimes be shown in a table. The following is an
example that shows how the number of gallons of gasoline (input values) relate
to the cost of the gasoline (output values).
Input (gallons) 9
12
13
17
Output
37.08
40.17
52.53
27.81
(dollars)
How much does a gallon of gas cost based on the data in the table?
Identifying a Function
Input
0
1
4
6
Input
0
0
5
10
Output
0
2
8
12
This pairing ____ a function because
each input is paired with exactly
only one output.
Output
2
3
4
5
This pairing ____ ______ a function
because input 0 is paired with both
outputs 2 and 3.
Write a function rule for a real- life situation
At a community center, guitar lessons are offered at night. The fee is $21 per
hour. You plan to attend 5 lessons. Write the amount you will spend as a
function of the number of lessons you will attend. Identify the independent and
dependent variables. Then identify the domain and range of the function.
Amount spent (dollars)
A
=
cost per lesson
(dollars per lesson)
=
●
number of lessons
(lessons)
●
21
L
We can show the amount you spend as a function of the number of lessons in a
table:
Number of
lessons
Amount
spent
1
2
3
4
5
21
42
63
84
105
The independent variable is __________________________, and the dependent
variable is _________________________. This is because the money you spend
depends on how many lesson you will attend.
The domain for this function is_________________________.
The range for this function is __________________________.
Guided practice:
1) Identify the domain and range:
Input: 0, 1, 2, 3
Output: 5, 7, 15, 44
Domain:___________________
Range: ___________________
2) Tell whether the following are
functions:
X Y Yes or No X Y
1 5
0 3
2 10
1 11
3 12
1 18
4 15
3 24
Yes or No
3) The domain of the function y = x
+ 3 is 1, 2, 3. What is the range of
the function?
4) Find the range of the function if the
domain of the function y = 4x
is 0, 1, 2, 3:
5.) In the equation p = t + 9, which
variable is the independent variable,
and which is the dependent variable?
6) Describe the relationship between
the input, x, and the output, y in this
table:
Independent: _______
Dependent: _______
Why?
x
y
0
2
1
3
2
4
3
5
7) Look at the relationship between x
and y in this table. Then try to write
an equation that relates the two
variables:
x
y
0
0
2
4
4
8
6
12
8) You make $9.50 an hour at your
summer job. In 4 hours of work, you
make ___________ dollars. Which is
the independent variable, the number
of hours or the amount of money you
make?
________________________
Homework: pgs 38-39 #2 – 16 even, 21