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FM Minimum Points

1.5 Use of Data and Graphs

Constructing Graphs from Tables

  • Given a table containing the x and y values of several points on a graph, we can construct a graph by plotting the known points and draw between them, using the trend of points to guess the overall shape of the graph.
  • When guessing the shape of the graph, there are many possible options. It is best to go with the simplest option.

Example

X

Y

0.5

11

1

8.5

1.5

5.5

2

4

3

2

4.5

1.8

6

1.2

9

1

We wish to construct a graph from the above table. To begin, we plot the points on a graph:

Picture 2

Now, we draw between these points. In this case, the overall trend appears to curve and so we will draw a curved line:

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1.4 Analysing Non-Linear Graphs

Intercepts of Non-Linear Graphs

  • Non-linear graphs can have no intercepts, one intercept or multiple intercepts along either axis.

Example

Picture 2

Above is a graph showing the profits earned by a community theatre in the years before they changed management. In the context of this situation, we can say that the intercepts at t=-3, -2 and 1 years represent points at which the community theatre just broke even (i.e. no profit or loss). The intercept at P=$1000 represents the profits made in the year the new management took over.

Maximum/Minimum Points

  • It may interest us to know the highest, or lowest values that the y-variable has taken. For example, if we want to find the highest a tide has been in a year in order to know how high to build a support structure.
  • The maximum and minimum points of non-linear graphs will be points of 0 gradient or the endpoints of a section (i.e. where a graph ends or undergoes structural change).
  • There may be multiple minimum points and/or multiple maximum points.
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