Function Families

Function Families

CRA Description : 
Students represent a real-world scenario as a function and describe how changing the parameters of the function likewise transforms the scenario. Students perform transformations to the function and describe how the transformations affect all representations of the function (graph, table, function notation, and context).
Subjects: 
Mathematics
Algebra II
Pre-Calculus
Key Concepts and Terms: 
Asymptote
Domain / Range
Even / Odd Function
Inverse Function
Parameter
Parent Function [Including Linear, Quadratic, Cubic, Square Root, Reciprocal, Absolute Value, Exponential, and Logarithmic (Also Trigonometric and Inverse if Trigonometric if Appropriate)]
Transformation [Including Horizontal/Vertical Shift (Translation), Stretch/Compress (Dilation), Reflection]
Prior Knowledge: 
Fluency with all forms of algebraic representation (symbolic, graph, table, context) is assumed. Students are expected to support their investigation using a graphing calculator or mathematical software. Students should have experience with functions including function notation, graphing, domain and range, tables of values, and inverses (if applicable). Prior knowledge of the parent functions will vary. Algebra II students will have knowledge of linear, quadratic, and exponential functions, and may have learned about square root, logarithmic, absolute value, and reciprocal functions. For pre- calculus students, the parent functions included for advanced studies are all of the above and basic trigonometric and inverse trigonometric functions.

Comments

This CRA is coded for an Algebra II level course. However, with the upcoming TEKS changes on the transformations on linear, quadratic, and exponential functions moving down into Algebra I, this CRA will be more fitted for use in Algebra I. This allows the students to review the parent functions, and then look at how they can be manipulated to different functions. This would be help relate these transformations as something that happens with all of the functions. In order for me to use it with the Algebra I students, I will need to remove a few of the function families. I would only need to use it for linear functions, quadratic functions, and exponential functions. 

Submitted by NikLee33 (not verified) on