(After Test 1)
Topics:
• Even and odd functions
Even and odd functions are classified by their symmetries.
• A function is even if 
• A function is odd if 
Another way to describe the symmetry of an odd function: if you reflect over the y-axis and then over the x-axis, the graph comes back to its original position.
Three videos are linked below: they are very good, but being on YouTube, it is possible that other videos may start autoplaying after they end. I apologize if that happens. I don’t know how to make it stop.
Here is a video that shows how the algebraic definition relates to the symmetry of the graph
And here is a very good video explanation of the symmetries of even and odd functions
And here is a video that shows the symmetries very nicely (except that at one point she seems to say that a graph represents a function when that graph fails the vertical line test! But apart from that it is highly recommended!)
There are functions which are neither even nor odd. In fact, being even or odd is rather special.
• Operation on functions: composition of functions, starting with Definition 6.5 on p. 78. We did not have time to discuss the domains of composite functions. You have to be a little careful with these, because the domains of the composite functions are not always what you would think they were. We will return to this next time.
Homework:
• Review even and odd functions, the algebraic definition and the symmetry of each type. You should be able to recognize the graph of an even or odd function by its symmetry, and also be able to check algebraically if a function given by a formula os even, odd, or neither. See Definition 5.9 and Example 5.10 (which we discussed in class).
• Review composition of functions, starting with Definition 6.5 on p. 78 in the textbook and through the end of section 6.1. (Notes will be posted soon, the assignment follows in this post.) You may want to read this post on Composition of Functions from Math is Fun as well.
• Do the following problems in the textbook: from the Course Outline : the assigned parts of Exercises 5.5 and 6.3-6.5 (see the course outline to know which parts to do) – also mae sure you have done the homework assigned last time!
• Start on the WeBWorK, which is not due until next Tuesday, but you should assume that problems 1-3 are due by Sunday night. The others (#4-5) require discussion of domains of composite functions: you can try them if you like, but they are not due until Tuesday.
• There will be a quiz on Monday. The topic will be transformations of basic functions and even and odd functions.
Don’t forget, if you get stuck on a problem, you can post a question on Piazza. Make sure to give your question a good subject line and tell us the problem itself – we need this information in order to answer your question. And please only put one problem per posted question!
