Relating Graphs and Events

“WALT…”
◦ Interpret, sketch, and analyze graphs from
situations

3 < x + 2 < 10

10 > -2x + 4 > 19

-5 ≥ ½ x + 3 > 11
Use the graph at the right.
Name the point with the given coordinates.
1. (4, –2)
2. (4, 3)
3. (2, –4)
4. (–2, 1)
Name the coordinates of each given point.
5. B
6. F
7. G

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.
This graph shows someone taking a walk in
the neighborhood. Describe what it shows by labeling each
part.
A pelican flies above the water searching for fish. Sketch a
graph of its altitude from takeoff from shore to diving to the
water to catch a fish. Label each section.
In your math notebook write what you think
this graph tells you.
Deaths

Percent of people using shaving cream
Which graph in Example 3 could show a car sitting at a
stoplight?
Graph I indicates a quantity that does not change with time.
Graph II shows an increase over time.
A car sitting at a stoplight would stay in the same place over time.
Graph I could show a car sitting at a stoplight.

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.
Use the graph for questions 1–3.
1. Why does this graph not start at zero?
A person’s height is not zero when born.
2. Why is the graph not a straight slanted line?
A straight line represents a constant rate of growth and
people do not grow that way.
3. What does the flat part at the top of the graph
represent?
The person has stayed the same height over a long period of time.
4. Would a horizontal line, a straight slanted line, a curve, or a jagged
curve best represent the calories you burn during the day?
a jagged curve

Step 1: Determine important information.


Step 1: Determine important information.
Step 2: Determine dependent and
independent variables.



Step 1: Determine important information.
Step 2: Determine dependent and
independent variables.
Step 3: Find starting point.
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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 Katniss 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 Katniss 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

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?
◦ Katniss 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?
◦ Katniss 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 ___________________