Summer Assignment

I'm in the middle of writing a summer assignment for Honors Pre-Calculus students and I need your help! I haven't taught this course before, and the only Algebra 2 I've taught was a CP class that struggled.  The current summer assignment is a random assortment of problems that neither of us who will be teaching the course next year want to assign, let alone grade!  So, here is what I have so far, major inspiration taken from @mgolding's project: Function Family Album.  Feel free to skim or skip right to my questions at the bottom to see what I'm requesting feedback on.

Summer Assignment

Your mission is to create a resource which summarizes the types of functions you learned about in Algebra II.  This assignment will give you an opportunity to showcase your creativity, but will also be an excellent reference for you to use throughout the course; so be sure to include enough information to refresh your memory on all the topics included.

You may choose any format you like to present this information (poster, pamphlet, scrapbook or anything else you can think of) so long as it includes all the required aspects.

Families of Functions:

Linear, Absolute Value, Quadratic, Cubic, Exponential, Radical, Logarithmic, Rational

For each family you will provide the following information:

• Parent Function graph (ex: f(x)=x^2)
• One shift (horizontal or vertical)
• One stretch or shrink

When you have completed this section you will have 18 graphs all labeled with a title, an equation in function notation and a description.  Be sure to have at least one of each type of transformation (horizontal and vertical shifts, stretch and shrink) among all the graphs.

Choose one of the following:

*Coming soon* (equations for cubic that’s increasing and decreasing, quadratic with x intercepts, radical with x and y intercepts etc.)

For this function you will provide more detail:

• Graph and table of values
• Domain and range
• Intercepts (x and y)
• Intervals of increasing and decreasing
• Maxima and minima (local and/or global)
• End behavior
• Whether or not each of the following points is on your curve *coming soon* (list points where at least one is on each option)
• Value of function at x=__ and y=__ *coming soon*
• Make up a situation that this graph might describe (feel free to be as silly or serious as you like; if your function looks like someone’s velocity as they fly to the moon write that! Just provide enough detail to match parts of the story to parts of the graph)

Does this seem like too much?  Do I encourage technology or require them to graph by hand?  I obviously need to fill in some functions and other details.  Do you have a favorite function that would work well for the last section?  Is this enough detail if I provide an example on my course webpage?  We will also be available via email and have a few summer sessions at the coffee shop in town.