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. 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 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. 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 ___________________