Relating Graphs and Events

Goals / “I can…”◦ 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.

A big part of math is understanding the world around us.

Part of understanding the world around us is representing information mathematically.

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 inthe 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.

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 cost depends on the number of pairs.The dependent variable (x) is the cost.The independent variable (y) is the number of pairs.The 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?

2. Why is the graph not a straight slanted line?

3. What does the flat part at the top of the graph

represent?

A person’s height is not zero when born.

A straight line represents a constant rate of growth and people do not grow that way.

The person has stayed the same height over a long period of time.

a jagged curve

4. Would a horizontal line, a straight slanted line, a curve, or a jagged

curve best represent the calories you burn during the day?

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.

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?

TIME TIME TIME

SPEED

SPEED

SPEED

GRAPH 1 GRAPH 2 GRAPH 3

What information can we use?

TIME TIME TIME

SPEED

SPEED

SPEED

GRAPH 1 GRAPH 2 GRAPH 3

What information can we use?◦ Kim starts off going a steady speed…meaning it

does not change.

TIME TIME TIME

SPEED

SPEED

SPEED

GRAPH 1 GRAPH 2 GRAPH 3

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.

TIME TIME TIME

SPEED

SPEED

SPEED

GRAPH 1 GRAPH 2 GRAPH 3

Time (seconds) 0 0.5 1.0 1.5 2.0 2.5 3.0Height (feet) 200 196 184 164 136 100 56

Year 1983 1985 1987 1989 1991 1993 1995

Cost (cents) 22 25 25 25 29 29 32

•Height of Falling Object

•Costs of First Class Postage Stamps.

Graph 1 Graph 2 Graph 3 Graph 4

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 ___________________