Module 4 Summary
Module 4 Summary
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A coach can use performance analysis to provide feedback to an athlete about training and skills. Performance analysis is an area of sport science that enables a coach to use statistical and video data to help an athlete or team of athletes improve. An athlete can use the information to perfect techniques, increase strength and speed, and develop winning strategies.
Performance analysis is a growing industry that has spawned both software products and consulting groups. Much research goes into the development of these software tools. Consultants, too, are well versed in the research and can explain how an assortment of variables will affect an athleteβs performance.
In order to be a successful performance analyst, an athlete, coach, or consultant must have a sound understanding of relations and of how one variable will affect another. The analyst must know how to analyze trends and to interpret graphs.
In this module you were introduced to relations. You learned how to differentiate between independent and dependent variables. You also learned how to sketch graphs representing specific circumstances as well as how to interpret graphs of relations. Examples demonstrated when it is appropriate to connect the points on a graph and when it is inappropriate.
You learned about a special group of relations known as functions. You learned that not all relations are functions and investigated how you can identify graphs, sets of ordered pairs, and arrow diagrams as functions.
You also examined how you can describe the elements of a relation using the concepts of domain and range. You learned that for a given relation, all possible values of the independent variable are collectively known as the domain and all possible values of the dependent variable are known as the range. Words, lists, set notation, and interval notation can all be used to express domain and range.
In the second half of the module you learned that slope is a measure of the steepness of a line. You analyzed the rise and run of a staircase and used an applet to explore the different orientations of a line. You discovered that slope can be expressed in many ways that are all equivalent to 
You also investigated slope as a rate of change and discovered that the units of any slope are precisely the ratio comparing the units of the independent variable to the dependent variable. You used slopes with their units to solve contextual problems.
Throughout the module, you had opportunities to work on a project. From the investigation of graphs of epidemics to measuring your heart rate to the investigation of slopes in sports, you have engaged in multiple inquiry activities which have supported your learning of relations and functions.
The Outcomes for Module 4 table summarizes the learning outcomes in this unit. As a review of what you have learned, complete the table by identifying those activities that you undertook to address the corresponding outcomes. Save a copy of this completed table with your work from this module in your course folder.
In Module 5 you will continue to investigate relations, but you will focus specifically on linear relations. Linear relations are represented by graphs of straight lines. As such, you will continue to study slopes of lines and how these slopes can be used to determine the equations of lines. You will continue to work with graphs and other representations of linear representations such as words, tables, and ordered pairs.