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5.1

5.1. Relating Graphs and Events. 5.1 – Relating Graphs & Events. Goals / “I can…” Interpret, sketch, and analyze graphs from situations. In your math notebook solve the compound inequalities:. 3 < x + 2 < 10 10 > -2x + 4 > 19 -5 ≥ ½ x + 3 > 11. Relating Graphs to Events.

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5.1

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  1. 5.1 Relating Graphs and Events

  2. 5.1 – Relating Graphs & Events Goals / “I can…” Interpret, sketch, and analyze graphs from situations

  3. In your math notebook solve the compound inequalities: • 3 < x + 2 < 10 • 10 > -2x + 4 > 19 • -5 ≥ ½ x + 3 > 11

  4. Relating Graphs to Events 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.B6.F7.G

  5. Relating Graphs and Events • 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.

  6. Relating Graphs and Events • A big part of math is understanding the world around us.

  7. Relating Graphs and Events • A big part of math is understanding the world around us. • Part of understanding the world around us is representing information mathematically.

  8. Relating Graphs and Events • 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.

  9. Relating Graphs to Events This graph shows someone taking a walk in the neighborhood. Describe what it shows by labeling each part.

  10. Relating Graphs to Events 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.

  11. Understanding the graph: • In your math notebook write what you think this graph tells you. Deaths Percent of people using shaving cream

  12. Relating Graphs to Events Graph I indicates a quantity that does not change with time. Graph II shows an increase over time. Which graph in Example 3 could show a car sitting at a stoplight? A car sitting at a stoplight would stay in the same place over time. Graph I could show a car sitting at a stoplight.

  13. Relating Graphs and Events • 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.

  14. Relating Graphs and Events • 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.

  15. Relating Graphs and Events • 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. 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.

  16. Draw out the graph.

  17. Draw out the graph. 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.

  18. Represent the information with a graph: • A balloon is being inflated with air. As more air is pumped into the balloon, the volume increases until it finally bursts.

  19. Represent the information with a graph: • 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.

  20. Represent the information with a graph:

  21. Relating Graphs to Events 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. 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

  22. Steps to solving with graphs: • Step 1: Determine important information.

  23. Steps to solving with graphs: • Step 1: Determine important information. • Step 2: Determine dependent and independent variables.

  24. Steps to solving with graphs: • Step 1: Determine important information. • Step 2: Determine dependent and independent variables. • Step 3: Find starting point.

  25. Steps to solving with graphs: • Step 1: Determine important information. • Step 2: Determine dependent and independent variables. • Step 3: Find starting point. • Step 4: Represent graphically.

  26. Which graph works best? •  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?

  27. GRAPH 3 GRAPH 2 GRAPH 1 SPEED SPEED SPEED TIME TIME TIME Which graph works best? •  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?

  28. GRAPH 3 GRAPH 2 GRAPH 1 SPEED SPEED SPEED TIME TIME TIME Which graph works best? • What information can we use?

  29. GRAPH 3 GRAPH 2 GRAPH 1 SPEED SPEED SPEED TIME TIME TIME Which graph works best? • What information can we use? • Kim starts off going a steady speed…meaning it does not change.

  30. GRAPH 3 GRAPH 2 GRAPH 1 SPEED SPEED SPEED TIME TIME TIME Which graph works best? • 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.

  31. Graph 1 Graph 4 Graph 2 Graph 3 What graph is best for the tables of data? • Height of Falling Object • Costs of First Class Postage Stamps.

  32. Sketch a reasonable graph for the situation described (be sure to label your axes), identify the dependent and independent variables, and complete the statement. • 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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