ADAPTING GRAPHS 3rd year of secondary education

 1.CHANGING MAXIMUM AND MINIMUM POINTS In the following window there is a graph which is made up of several lines joined together. Use the mouse to change the vertical position of the ends of these lines. 1.- There are no values given in this first activity. We just have to look at the points shown in the window and the shape of the graph which is drawn. Change the parameter values so that: a.- We get the graph of a constant function. b.- We get a graph which is increasing. c.- We get a graph which is decreasing. d.- We get a graph which is increasing-constant-decreasing-increasing. e.- We get a graph which is decreasing-increasing-decreasing-constant.   Draw these different graphs into your notebook and indicate their maximum and minimum points as well as the intervals of increase and decrease. 2.- Write down different situations which could be represented by each of the graphs in the last activity.

2. NOW LET'S USE  REAL DATA

As with one of the graphs on the previous page, in this window you can change the vertical position of all the points from M1 to M12. You can also see numerical data on this graph, which you will need to complete the following activities. Imagine that the graph represents the balance of a bank account of a photographic and reprographic service during the year 2000 (in thousands of euros (€)).

This will make it easier to focus more clearly on the possible answers to the activities.

3.- In your exercise book draw up a table of values which shows the balance at the end of each of the twelve months (the white points on the graph) and draw the graph which corresponds to this information.

4.- In which months do the maximum points of the graph fall? What about the minimum points? During which months was business at its best (refer to the change in balance)?

5.- Change the position of points M1 to M12 so that the graph represents the information given in the following table of values:

 month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec balance (in thousands of €) 20.43 38.30 125.84 105.18 162.99 137.02 165.28 208.48 106.56 174.82 193.07 226.32

6.- Draw the graph from this last activity into your exercise book and mark on it the maximum and minimum points and the intervals of phases of increase and decrease.

3. BACK TO SPORT

In the following window there is a graph which illustrates the outline of an area, between two Spanish towns 50 km apart, where a cycling race takes place every year.

 7.- In your exercise book draw the graph of the route, clearly indicating the following: a wood which is found at the highest point of the route, a stream which crosses the second lowest point of the route, the town where the race begins (Villarrubias), the town where the race ends (Zalacaín) and a hotel which is at an altitude of 300 metres and coincides with one of the minimum points of the graph. 8.- Work out the value of the slope in each of the stages of the race. To work this out divide the difference in height (always positive, never negative !!) by the horizontal distance of each of the relevant stages and multiply the result by 100. For example, if we go up a ramp whose difference in height between the top and the bottom is 150m and the horizontal distance of the ramp from beginning to end is 1 km (1,000 m), the slope is 15%.

9.- In the window there is also a white jointed line whose connecting points can be moved vertically. Change the position of these points so that the line represents the approximate change in speed during this stage of the race. (Neither values for speed nor time appear on the graph). Then, copy the graph into your exercise book indicating clearly the maximum and minimum points and the intervals of increase and decrease. What connection is there between the two graph that have been plotted?

10.- Change the position of all the points from A to H until you get the outline of the race, but backwards, i.e. as if it had begun in Zalacaín and finished in Villarubias.

 Josep Mª Navarro Canut Spanish Ministry of Education. Year 2001