Transcript Relating Graphs and Events - Mr. Lothamer's Classes:


3 < x + 2 < 10

10 > -2x + 4 > 19

-5 ≥ ½ x + 3 > 11
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Now that you have worked with both
equations and inequalities, you will begin to
learn more about functions and their
characteristics. One of those characteristics
is their graphs. This lesson is an introduction
relating graphs to events that will later lead
to understanding functions.

A big part of math is understanding the world
around us.
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
A big part of math is understanding the world
around us.
Part of understanding the world around us is
representing information mathematically.
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

A big part of math is understanding the world
around us.
Part of understanding the world around us is
representing information mathematically.
In life graphs are often used to persuade
people.
In your math notebook write what you think
this graph tells you.
Deaths

Percent of people using shaving cream
In your math notebook write what you think
this graph tells you.
Number of people
Hit by a falling piano
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Age

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. Make a table showing
the cost of 1 to 4 pairs of shoes.

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. Make a table showing
the cost of 1 to 4 pairs of shoes.
Number of Pairs
Total Cost
1
40
2
60
3
70
4
75

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. Make a table showing
the cost of 1 to 4 pairs of shoes.
Number of Pairs
Total Cost
1
40
2
60
3
70
4
75
The
The
The
The
cost depends on the number of pairs.
dependent variable (x) is the cost.
independent variable (y) is the number of pairs.
cost is a function of the number of pairs
Sketch a graph that represents this situation.
Label each axis and indicate the units.
Note: The points are not connected since shoes can only be
purchased in discrete units (1 pair, 2 pairs, etc.). You can not
purchase 1.5 pairs of shoes.

A balloon is being inflated with air. As more
air is pumped into the balloon, the volume
increases until it finally bursts.

A balloon is being inflated with air. As more
air is pumped into the balloon, the volume
increases until it finally bursts.
◦
◦
◦
◦
Determine the dependent and independent variables
Sketch a graph that represents this situation.
Label each axis.
Determine if the function is discrete or continuous.

Step 1: Determine important information.


Step 1: Determine important information.
Step 2: Determine dependent and
independent variables.
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

Step 1: Determine important information.
Step 2: Determine dependent and
independent variables.
Step 3: Find starting point.
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
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
Step 1: Determine important information.
Step 2: Determine dependent and
independent variables.
Step 3: Find starting point.
Step 4: Represent graphically.

For a certain time Kim Possible jogs up a hill
at a steady speed. Then she runs down the
hill and picks up her speed. Which graph
below accurately represents this situation?

For a certain time Kim Possible jogs up a hill
at a steady speed. Then she runs down the
hill and picks up her speed. Which graph
below accurately represents this situation?
SP
EE
D
SP
EE
D
TIME
GRAPH 3
GRAPH 2
GRAPH 1
SP
EE
D
TIME
TIME
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What information can we use?
SP
EE
D
SP
EE
D
TIME
GRAPH 3
GRAPH 2
GRAPH 1
SP
EE
D
TIME
TIME

What information can we use?
◦ Kim starts off going a steady speed…meaning it
does not change.
SP
EE
D
SP
EE
D
TIME
GRAPH 3
GRAPH 2
GRAPH 1
SP
EE
D
TIME
TIME

What information can we use?
◦ Kim starts off going a steady speed…meaning it
does not change.
◦ After she reaches the top she speeds up.
SP
EE
D
SP
EE
D
TIME
GRAPH 3
GRAPH 2
GRAPH 1
SP
EE
D
TIME
TIME
•Height of Falling Object
Time (seconds)
Height (feet)
Year
Cost (cents)
Graph 1
0
0.5
1.0
1.5
2.0
200
196
184
164
136
•Costs of First Class Postage Stamps.
1983
22
1985
25
Graph 2
1987
25
1989
25
Graph 3
1991
29
Graph 4
2.5
100
3.0
56
1993
29
1995
32

The amount of force, f, used to hit your
thumb with a hammer, impacts the amount of
pain, p, that you experience
Dependent Variable: ____________________
Independent Variable: ___________________
___________________ is a function of ___________________
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Handout
Due Wednesday