Session 1, Part C:
Qualitative Graphs

In This Part: Introduction to Qualitative Graphs | The Bus Stop Queue | Going to School
Descriptive Graphs | Filling Bottles

Problem C5

Often we are asked to sketch graphs from words or descriptions. Choose the best graph to fit each of the situations described below. Note 10

 a. I really enjoy cold milk or hot milk, but I loathe lukewarm milk. b. Prices are now rising more slowly than at any time during the last five years. c. The smaller the boxes are, the more boxes we can load into the van. d. After the concert there was a stunned silence. Then one person in the audience began to clap. Gradually, those around her joined in, and soon everyone was applauding and cheering. e. If the price for movie admission is too low, then the owners will lose money. On the other hand, if admission is too high, then few people will attend, and again the owners will lose. A movie theater must therefore charge a moderate price in order to stay profitable. f. Make up three stories of your own to fit three of the remaining graphs.

 At each important place on the graph, think about whether the values in the graph should be increasing more rapidly, increasing but slowing down, remaining steady, decreasing but leveling off, or decreasing more rapidly. Additionally, the graph should reflect important changes in the real-world situation and the starting position of the graph (where it touches the axes).   Close Tip At each important place on the graph, think about whether the values in the graph should be increasing more rapidly, increasing but slowing down, remaining steady, decreasing but leveling off, or decreasing more rapidly. Additionally, the graph should reflect important changes in the real-world situation and the starting position of the graph (where it touches the axes).

 Video Segment In this segment, Professor Cossey and participants discuss different answers to Problem C5(a), especially the labeling of the axes. One group selected graph number 11 as its answer. How could you defend this choice? How did the group label the axes? You can find this segment on the session video, approximately 19 minutes and 44 seconds after the Annenberg Media logo.

Problem C6

In the following real-world situations, decide what happens. Explain each situation carefully in words, and then choose the graph that best represents the situation, as in Problem C5.

 a. How does the cost of a bag of potatoes depend on its weight? b. How does the diameter of a balloon vary as air is slowly released from it? c. How does the time for running a race depend upon the distance run in the race? d. How does the speed of a child vary on a swing? e. How does the speed of a ball vary as it bounces along?

 As in Problem C5, consider carefully where the graph should begin, whether it should increase or decrease, and how quickly.   Close Tip As in Problem C5, consider carefully where the graph should begin, whether it should increase or decrease, and how quickly.

Problem C7

Draw the graphs to illustrate the following statements. Label your axes with the variables they represent.

 a. In the spring, my lawn grew very quickly, and it needed cutting every week. But since we have had this hot dry spell, it needs cutting less frequently. b. When doing a jigsaw puzzle, I usually spend the first half hour or so just sorting out the edge pieces. When I have collected together all the ones I can find, I construct a border around the edge of the table. Then I start to fill in the border with the center pieces. At first this is very slow going, but the more pieces you put in, the less you have to sort through, and so the faster you get.

 Problem C8 Choose at least three of the situations in Problems C5-C7, and change the conditions in a way that alters the graph of the situation. Then, draw the new graphs.

 Problems in Part C are taken from The Language of Functions and Graphs, by Malcolm Swan and the Shell Centre Team (Nottingham, U.K.: Shell Centre Publications, 1999).