This final lesson in Unit #3 introduces students to the two fundamental sets involved in the function process, the domain and range. Technical definitions are given and then we work with a variety of examples, both applied and standard. I’ve already had it suggested that this topic would be better off at the beginning of the unit so that students could use the terminology throughout the unit. What do others think?
This extremely important idea is introduced for the first time in this lesson. We initially develop the concept by looking at a motion problem (naturally) and then present the classic equation. I worry that the equation may be too symbol heavy and would love to hear how this lesson went for students/teachers.
In this lesson we finally break out the graphing calculator in order to use the TABLE feature to graph functions. We use the TI-84+ (with TI-SmartView) in the video, which will certainly be a disadvantage for students with other models and makes. I’m hopeful this still works for most students. I particularly like the idea that students can watch the video repeatedly to learn how to use the technology properly.
This lesson contains a ton of terminology on the graphical features of functions. These include intercepts/zeroes, relative and absolute maxima and minima, intervals of increase/decrease, and intervals of positive and negative. Numerous graphs are both given and generated by students in order to reinforce this terminology.
In this lesson, we look at how to translate equations of functions into their graphs by producing input/output tables. We do not yet use graphing calculator technology in this lesson, but it is coming soon. And, for the first time, we introduce the very trick concept of a piecewise defined function. Although this may seem early, we use them on and off for the rest of the course, so the early exposure is just the beginning.
In this lesson we examine f(x) notation and how to interpret it in various contexts. The notation is first used with an function rule given by an equation. Then it is expanded to include both a tabular and graphical example. This was one of the first screencast videos I made and takes place in front of my daughter’s curtains. I’m not even wearing my red shirt in this one.
In this lesson we look at the classic definition of a function and then see it applied with an equation, a table, and a graphical example of a function. Real world examples in the case of the table and the graphical function help root the concept of a function in scenarios that students can relate to.
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