Name:
Period #: _______ Date: ____________________
Notes……Unit 2.9 Direct and Inverse Variation Comparison
Objective:
To compare the direct and inverse variation.
In the last section we investigated the relationship between the distance from an object and its apparent size.
We found a decreasing non-linear relationship. Let’s answer some questions…
1. What function rule describes the relationship between the distance from a meter stick and its apparent
size from our investigation yesterday?
2. What function rule describes the relationship between the length and width of a rectangle that has an
area of 20 square units?
3. What do these function rules have in common?
How do they differ?
4. Graph the functions on separate axes. Sketch your graphs.
5. What do the graphs have in common?
How do they differ?
6. As the independent variable increases, what happens to the dependent variable in each situation?
Does this change happen at a constant rate?
7. Think back to the apparent size situation in the last section. The table below contains some sample data
that one student group collected.
For each pair, multiply the
Distance from meter stick (m) Apparent Size(cm) x·y y
apparent length of the stick
x
by the distance from it.
8
24.5
Record your results in the
10
19.5
12
16.3
14
14
table where appropriate.
Then divide the apparent
size from the distance and
record it in the last column.
8. If the values in the third column are really close but not exact, find the average of the products of the
distance from the meter stick and its apparent length? What does this mean about the relationship?
9. Are the values in the fourth column close? What does this mean about the relationship?
10. Is the relationship between distance from the meter stick and apparent size a proportional relationship?
How do you know?
11. Use your graphing calculator to make a scatterplot of apparent size versus distance from the stick.
Sketch your graph and identify your window.
x
y
1
196
2
98
3
65.33333
4
49
5
39.2
6
32.66667
Xmin: ____
Xmax: ____
Xscl: ____
Ymin: ___
Ymax: _____
Yscl: _____
SUMMARY: In some relationships, the product of the values of the independent variable and the
corresponding values of the dependent variable is a constant. In other words, xy equals (or close to) a constant,
k. These relationships are called inverse variation or indirect variation. In these situations, the variables are
said to be inversely proportional.
k
The general form of an inverse variation function rule is y  . The parent function for inverse variation
x
1
functions is y  , and the graphs of this family of functions have two branches.
x
Direct Variation
Inverse Variation
Assignment: Unit 2.9 Classwork (All problems)