2.  3 < x + 2 < 10  10 > -2x + 4 > 19  -5 ≥ ½ x + 3 > 11

3.  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.

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

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

6.  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.

7.  In your math notebook write what you think this graph tells you. Deaths Percent of people using shaving cream

8.  In your math notebook write what you think this graph tells you. Number of people Hit by a falling piano Age

9.  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.

10. Number of PairsTotal Cost 140 260 370 475

11.  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 PairsTotal Cost 140 260 370 475 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.

13. 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.

15.  A balloon is being inflated with air. As more air is pumped into the balloon, the volume increases until it finally bursts.

16. ◦ Determine the dependent and independent variables ◦ Sketch a graph that represents this situation. ◦ Label each axis. ◦ Determine if the function is discrete or continuous.

19.  Step 1: Determine important information.

20.  Step 2: Determine dependent and independent variables.

21.  Step 1: Determine important information.  Step 2: Determine dependent and independent variables.  Step 3: Find starting point.

22.  Step 1: Determine important information.  Step 2: Determine dependent and independent variables.  Step 3: Find starting point.  Step 4: Represent graphically.

23.  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?

24. TIME SP EE D GRAPH 1 GRAPH 2 GRAPH 3

25.  What information can we use? TIME SP EE D GRAPH 1 GRAPH 2 GRAPH 3

26.  What information can we use? ◦ Kim starts off going a steady speed…meaning it does not change. TIME SP EE D GRAPH 1 GRAPH 2 GRAPH 3

27.  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 SP EE D GRAPH 1 GRAPH 2 GRAPH 3

28. Time (seconds)00.51.01.52.02.53.0 Height (feet)20019618416413610056 Year1983198519871989199119931995 Cost (cents)2225 29 32 Height of Falling Object Costs of First Class Postage Stamps. Graph 1 Graph 2Graph 3 Graph 4

29.  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 ___________________

30.  Handout  Due Wednesday