Function Family Album & ScrapbookThis project covers the following standards:MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

a. Represent functions using function notation. b. Graph the basic functions f(x) = xn where n = 1 to 3, f(x) =√x, f(x) =│x│, and f(x) = 1/x. c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes. d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior. e. Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

Goal: Create a scrapbook for six function families. Your scrapbook will include detailed graphs, characteristics, the effects of transformations, and tables of values.

A family photo album tells the visual story of a family. Your album will tell the visual story of 6 families:

Linear Absolute Value Quadratic Cubic Radical Rational

Because each function is the parent of a family, you will also investigate the function’s children. For example, linear functions have 3 children, shown below:

So, there you have it: make a family album for all 6 families, including listing their children and everyone’s statistics. Refer to the rubric to learn how to complete the project.

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Children

Parent Linear

Vertical Shift Stretch & Shrink

Reflect (across x-

axis)

[This project is a metaphor, which is language that connects unrelated subjects. The metaphor here is that every function is described as a family using the language of families to help you understand functions. “America is a melting pot” is an example of a metaphor.]

Sample Page: Linear Function

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This vertical stretch increases the slope of the line by 2

This vertical shift of +3 increases the y-intercept by 3.

If I were a function, I would

be approximately f(x) = -2x

Straight Line (but we call him “Dad”)

RubricProject: Function Family Album & Scrapbook Date: ________________________________

Student(s): _________________________________________________________________________

Standard What it means for this project PointsMM1A1a Represent functions using function notation

Use f(x) notation whenever giving a function. 10%

MM1A1b Graph the six parent functions

For each parent function, draw an accurate graph showing the x-axis from -5 to 5 (no approximate sketches, please).

25%

MM1A1c Graph transformations of the six parent functions

For each parent function, demonstrate all the transformations (vertical shifts, stretches/shrinks, reflections across x-axis) on a graph.

25%

MM1A1d Investigate/Explain characteristics of a function: domain, range, zeros, intercepts, intervals of increase & decrease, maximum & minimum values, and end behavior

Describe the characteristics of the parent functions as well as how each transformation affects each characteristic. For example, “a vertical shift of n units on a linear graph changes the y-intercept by n units.”

You may show this with a picture (graph) or describe it using words.

25%

MM1A1e Relate to a given context the characteristics of a function and use graphs/tables to investigate behavior

For each parent function, provide a picture (from a magazine, for example) that resembles the function. Provide either a table of possible values OR list all the characteristics (see MM1A1d, above for a complete list). Note: for variety, the overall project must include 3 tables and 3 lists of characteristics.

15%

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