Unpacked Content
Knowledge
Students know:
- Techniques to find key features of functions when presented in different ways.
- Techniques to convert a function to a different form (algebraically, graphically, numerically in tables, or by verbal descriptions).
- Characteristics of linear and nonlinear functions.
Skills
Students are able to:
- Accurately determine which key features are most appropriate for comparing functions.
- Manipulate functions algebraically to reveal key functions.
- Convert a function to a different form (algebraically, graphically, numerically in tables, or by verbal descriptions) for the purpose of comparing it to another function.
- Compare functions based on their properties.
Understanding
Students understand that:
- Functions can be written in different but equivalent ways (algebraically, graphically, numerically in tables, or by verbal descriptions).
- Different representations of functions may aid in comparing key features of the functions.
- Functions are relationships between two variables that have a unique characteristic, that being, for each input there exists exactly one output.
- Functions can be represented in a variety of ways (graphs, tables, and equations), each of which provides unique perspectives of the relationship between the variables.
- Linear functions have a defining characteristic of a unit rate or slope that other nonlinear functions do not have.
Vocabulary
- Linear function
- Exponential function
- Quadratic function
- Absolute value function
- Linear Piecewise function
- non-linear functions
