Characteristics of Functions
Virginia SOL MA.CF.1
Identify and analyze properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch their graphs.
What students need to be able to do
- Identify polynomial, rational, piecewise-defined, absolute value, radical, and step functions from an equation or graph using mathematical reasoning.
- Analyze the domain and range of polynomial, rational, piecewise-defined, absolute value, radical, and step functions.
- Determine roots (including complex roots) of polynomial, rational, piecewise-defined, absolute value, radical, and step functions.
- Identify intercepts of polynomial, rational, piecewise-defined, absolute value, radical, and step functions.
- Analyze symmetry of functions, including even and odd functions.
- Identify asymptotes (horizontal, vertical, and oblique/slant) of rational and other functions.
- Determine points of discontinuity in functions.
- Identify intervals where functions are increasing, decreasing, or constant.
- Analyze end behavior of functions.
- Identify relative and absolute maximum and minimum points of functions.
- Sketch graphs of polynomial, rational, piecewise-defined, absolute value, radical, and step functions.