---
title: "A.FGR.2: Linear Functions & Sequences (Georgia Mathematics standard)"
code: A.FGR.2
cite_as: Georgia Standards of Excellence, Mathematics, A.FGR.2
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/A.FGR.2
md_url: https://georgiahomeroom.org/standards/code/A.FGR.2.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/A.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
---

# A.FGR.2: Linear Functions & Sequences

Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs.

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

## Expectations

- **A.FGR.2.1**: Use mathematically applicable situations algebraically and graphically to build and interpret arithmetic sequences as functions whose domain is a subset of the integers.
- **A.FGR.2.2**: Construct and interpret the graph of a linear function that models real-life phenomena and represent key characteristics of the graph using formal notation.
- **A.FGR.2.3**: Relate the domain and range of a linear function to its graph and, where applicable, to the quantitative relationship it describes. Use formal interval and set notation to describe the domain and range of linear functions.
- **A.FGR.2.4**: Use function notation to build and evaluate linear functions for inputs in their domains and interpret statements that use function notation in terms of a mathematical framework.
- **A.FGR.2.5**: Analyze the difference between linear functions and nonlinear functions by informally analyzing the graphs of various parent functions (linear, quadratic, exponential, absolute value, square root, and cube root parent curves).

## Georgia Milestones coverage

- Algebra I (EOC). Functional & Graphical Reasoning. Construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena. Use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs. (about 12% of the test; 7 points)

## What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

- **Beginning**: Identify a term in an arithmetic sequence. Identify the graph of a linear function. Given the graph of a linear function, identify the domain and range. Given an equation in function notation, evaluate the function for a specified input. Identify a function as linear or non-linear.
- **Developing**: Identify a rule to describe an arithmetic sequence. Identify and interpret key characteristics of linear functions. Describe the domain and range of a linear function by using formal notation. Given a verbal description, create and evaluate an equation by using function notation. Compare a linear function to the parent linear function f(x) = x.
- **Proficient**: Solve real-life problems involving arithmetic sequences graphically and algebraically. Analyze the key features of linear functions to interpret real-life phenomena. Identify and interpret the domain and range of a linear function in the context of a real-life problem. Interpret function notation in the context of a real-life problem. Compare a non-linear function to the appropriate parent function.
- **Distinguished**: Solve real-life problems involving function notation, domain and range, and the comparison of functions.

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