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 increasingconstantdecreasingincreasing. e. We get a
graph which is decreasingincreasingdecreasingconstant.
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:
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. 




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 



Except where otherwise noted, this work is licensed under a Creative Common License