---
title: "PC.FGR.2: Rational & Piecewise Functions (Georgia Mathematics standard)"
code: PC.FGR.2
cite_as: Georgia Standards of Excellence, Mathematics, PC.FGR.2
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/PC.FGR.2
md_url: https://georgiahomeroom.org/standards/code/PC.FGR.2.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/PC.FGR.2.md
source_url: https://case.georgiastandards.org/ims/case/v1p1/CFDocuments/e9dd7229-3558-4df2-85c6-57b8938f6180
source_last_changed: 2024-10-09
data_built: 2026-09-18
publisher: Georgia Homeroom, a free public-interest project of Georgia Civic Data. Not affiliated with or endorsed by the Georgia Department of Education or any school district.
up: https://georgiahomeroom.org/standards/math/high-school.md
index: https://georgiahomeroom.org/standards/index.md
---

# PC.FGR.2: Rational & Piecewise Functions

Analyze the behaviors of rational and piecewise functions to model contextual mathematical problems.

- Subject: Mathematics
- Appears in: High School, https://georgiahomeroom.org/standards/math/high-school.md

## Expectations

- Analyze piecewise-defined functions using different representations.
  - **PC.FGR.2.1**: Graph piecewise-defined functions, including step functions and absolute value functions.
  - **PC.FGR.2.2**: Describe characteristics by interpreting the algebraic form and graph of a piecewise-defined function.
  - **PC.FGR.2.3**: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of piecewise-defined functions; interpret limits expressed in analytic notation.
- Analyze rational functions using different representations.
  - **PC.FGR.2.4**: Divide polynomials using various methods.
  - **PC.FGR.2.5**: Graph rational functions and identify key characteristics.
  - **PC.FGR.2.6**: Represent the behavior of a rational function using limit notation for vertical and horizontal asymptotes and end behavior.
  - **PC.FGR.2.7**: Represent the limit of a function using both the informal definition and the graphical interpretation in the context of rational functions; interpret limits expressed in analytic notation.
  - **PC.FGR.2.8**: Solve simple rational equations in one variable, and give examples showing how extraneous solutions may arise.
  - **PC.FGR.2.9**: Perform partial fraction decomposition of rational functions using non-repeated linear factors.

## Georgia Milestones coverage

No Georgia Milestones blueprint cites this standard.

Source: Georgia Standards of Excellence, published by the Georgia Department of Education at case.georgiastandards.org.