Mathematical Analysis · Characteristics of Functions
Virginia SOL MA.CF.1
Virginia SOL MA.CF.1 is part of the Characteristics of Functions strand in Mathematical Analysis (Math). Under this Standards of Learning objective, students identify and analyze properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch their graphs. Below is what MA.CF.1 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice MA.CF.1 for the Virginia SOL test.
What SOL MA.CF.1 means
Identify and analyze properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch their graphs.
Skills you’ll practice for MA.CF.1
- 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.
Key concepts covered by MA.CF.1
- polynomial functions
- rational functions
- piecewise functions
- absolute value functions
- radical functions
- step functions
- function identification
- domain
- range
- function analysis
- roots
- complex roots
- polynomial roots
- rational roots
- absolute value roots
- intercepts
- x-intercepts
- y-intercepts
- function intercepts
- polynomial intercepts
- symmetry
- even functions
- odd functions
- function symmetry
- polynomial symmetry
- asymptotes
- horizontal asymptotes
- vertical asymptotes
- oblique asymptotes
- discontinuity
- points of discontinuity
- removable discontinuity
- jump discontinuity
- infinite discontinuity
- increasing intervals
- decreasing intervals
- constant intervals
- function intervals
- monotonicity
- end behavior
- function behavior
- polynomial end behavior
- rational end behavior
- relative maximum
- absolute maximum
- relative minimum
- absolute minimum
- extrema
- critical points
- graphing functions
- polynomial graphs
- rational graphs
- piecewise graphs
- absolute value graphs
How to study and practice SOL MA.CF.1
Start with a quick diagnostic to see whether MA.CF.1 is already solid, then work each skill above with guided notes, flashcards, and SOL-style practice questions. For official released items, see our Virginia SOL practice tests guide and how to study for the SOL test.
Related Mathematical Analysis standards in Characteristics of Functions
Frequently asked questions about SOL MA.CF.1
What is Virginia SOL MA.CF.1?
SOL MA.CF.1 is a Mathematical Analysis Standard of Learning in the Characteristics of Functions strand. It expects students to identify and analyze properties of polynomial, rational, piecewise-defined, absolute value, radical, and step functions and sketch their graphs.
What skills does SOL MA.CF.1 cover?
SOL MA.CF.1 is assessed on 11 skills: 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.
What strand of Mathematical Analysis is SOL MA.CF.1 in?
SOL MA.CF.1 belongs to the Characteristics of Functions reporting strand of the Mathematical Analysis Virginia Standards of Learning.
How do I study and practice for SOL MA.CF.1?
Start with a diagnostic to see whether MA.CF.1 is already solid, then work the 11 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.