Name:
Period #: _______ Date: ____________________
Notes……Unit 2.8 Inverse Variation
Objective:
To discover the characteristics of inverse variation.
There is another relationship that we haven’t talked about. If you hold a pencil
or pen up in front of you and compare the size of the pencil to the size of me,
is a 6 inch pencil really close to my height?
Resources
Inverse variation – A
relationship in which one
variable decreases as the
other increases and the
product of the corresponding
values of the variables is a
constant.
Example: xy = k or y 
k
x
Let’s look at some data:
Distance
from meter
stick (m)
Apparent
Size(cm)
10
7.8
15
5.2
20
3.9
25
3.12
In a proportional relationship, y = kx is a direct variation function.
In an inverse variation, y 
k
, this is a relationship that is inversely proportional.
x
For each table of values determine an appropriate viewing window, create a scatterplot, write a function rule,
and graph your function rule over your scatterplot.
Example 1: Function Rule: __________
x
y
-3
3
-2
1
3
-5
-1
-10
1
10
2
5
3
3
1
3
Example 2: A group of students are planning a trip to see the Houston Dynamos play in the play-offs. The
cost to buy a block of seats is $1500. The block of seats are for a maximum of 50 students. This includes a bus,
the seat and a meal at the game.
First find the
cost per
student:
Number of
students
5
10
Cost per
student
x·y
15
20
25
30
35
40
45
50
Do the following:
a) Fill in the table (above) for the cost per student.
b) Which is the independent variable? __________________
c) Which is the dependent variable? ___________________
d) What is a reasonable domain for this situation? ______________
e) What is a reasonable range for this situation? _____________
f) Indicate an appropriate viewing window, create a scatterplot, write a function rule, and graph your
function rule over your scatterplot.
Function Rule: _________________
Xmin: ___
Xmax: ___
Xscl: ___
Ymin: ___
Ymax: ___
Yscl: ___
g) If 48 students buy tickets to the game, what is the cost per student?
Assignment: Unit 2.8 Classwork (All problems)