 # 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. 