**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.

I think this is fabulous. What are you using for logarithmic? I'd use log base2 of x, but I'd be interested in discussion on that. I'd use f(x)=1/x for the rational.

ReplyDeleteI definitely couldn't ask my (college) pre-calc students to do this before the course. I might use something similar it as a midterm assignment. Thanks!

That sounds like a useful assignment because then they can glance back throughout the year.

ReplyDeleteWhat about links to foldable sites or a couple of others to give them inspiration. ... Maybe you can require that at least one is done by hand and at least one is done by technology (if you like). ... Do you want to make it a requirement that it should fit in their notebooks (what if someone makes a poster ... is that okay, what will they do with it throughout the year).

Anyway. Love the assignment :)

I'll have to ask the Alg2 teachers what log they use the most. f(x)=1/x is a good choice, I should probably provide the parent functions to eliminate confusion.

ReplyDeleteShireen- love the idea of linking to foldables. Making something that fits into their notebook is definitely a good idea. I will ask the other teacher but I think requiring at least one to be done by hand (maybe the last, in depth one?) and the others by their preference sounds like a plan.

Thanks for your input!