1.2
Relation
Yesterday we defined a correlation as . . .
a relationship
Let's look at some other examples . . .
Ex 1: A shoe store is having a sale. the first pair of shoes sells for $40.
The second pair sells for half price, or $20. The next pair sells for half of
that, and so on.
a. Make a table showing the cost of
1 to 5 pairs of shoes.
Number of
Pairs
Total Cost
b. Write the data as a list of
ordered pairs.
(1,40) (2,60) (3,70)
(4, 75) (5, 77.50)
c. Draw the graph that shows
the relationship between the
number of pairs of shoes and the
total price.
d. Describe the relationship between the number of pairs
of shoes purchased and the total cost.
as the number of shoes increases the total cost increases
Ex 1: A shoe store is having a sale. the first pair of shoes sells for $40.
The second pair sells for half price, or $20. The next pair sells for half of
that, and so on.
Number of
a. Make a table showing the cost of
1 to 5 pairs of shoes.
b. Write the data as a list of
ordered pairs.
(1,40), (2,60), (3,70), (4,75), (5,77.50)
c. Draw the graph that shows
the relationship between the
number of pairs of shoes and the
total price.
Total Cost
Pairs
1
$40
2
$60
3
$70
4
$75
5
$77.50
80
Cost
60
40
20
0
1 2 3 4 5
Pairs of Shoes
d. Describe the relationship between the number of pairs
of shoes purchased and the total cost.
As the pair of shoe purchases increases the total cost increases.
Independent Variable - graphed on the horizontal axis (or x-axis)
also known as the input
What is the independent variable in the situation that we just discussed?
Dependent Variable - graphed on the vertical axis (or y-axis)
also known as the output
What is the dependent variable in the situation that we just discussed?
Relation - a set of ordered pairs.
{(1,40), (2,60), (3,70), (4,75), (5,77.50)}
{(1,40), (2,60), (3,70), (4,75), (5,77.50)}
Domain - the values of independent variables (or x values.)
{1, 2, 3, 4, 5}
Range - the values of the dependent variables (or y values.)
{40, 60, 70, 75, 77.50}
Depreciation
Age of Car
(Years Old)
Approximate Value
of Car
0 (New)
$24, 265.00
1
$18, 198.75
2
$14,922.98
3
$12,236.84
4
$10,034.21
5
$8,529.08
This shows how a typical car depreciates (loses value) over a
period of five years.
Describe the relationship between the age of the car and its value.
From the table, you can see that as the age of the car
increases, the value decreases.
Car Depreciation Over a
Five Year Period
$24000
y - axis
$16000
$8000
1
point on a graph.
2
3
4
5
Written in the form (x,y).
origin
x - axis
Describe the relationship between the age of the car and its value
using the graph.
Because the line on the graph is downhill, you can
see that as the age of the car
increases, the value decreases.
The value of the car is said to be a function of the age of the car.
Function - a relationship
between input and output.
Car Depreciation Over a
Five Year Period
$24000
$16000
$8000
1
2
3
4
5
Ordered Pair - a point on a graph.
(The output depends on the input.)
Written in the form (x,y).
What is the independent variable in this relation?
the age of the car
State the domain.
{0, 1, 2, 3, 4, 5}
What is the//
independent variable in this relation?
the value of the car
State the range.
{24265, 18198.75, 14922.98, 12236.84, 10034.21, 8592.08}
Ex.3 A balloon is being inflated with air. As more and more air
is pumped into the balloon, the volume increases until it finally
bursts. Make a sketch of a graph of the situation.
Ex.4 The price of gasoline at the pump is dependent on the
availability of fuel oil. Write a story about the relationship in
the following graph.
price of gas at pump
amount of fuel oil available
Ex.3 A balloon is being inflated with air. As more and more air
is pumped into the balloon, the volume increases until it finally
bursts. Make a sketch of a graph of the situation.
Volume
Amount of Air Pumped
Ex.4 The price of gasoline at the pump is dependent on the
availability of fuel oil. Write a story about the relationship in
the following graph.
Sample story: When fuel oil is
scarce, the prices are high. As more
becomes available, the prices drop.
There is, however, a price below which
no gas station will set its price.
price of gas at pump
amount of fuel oil available