---
title: "8.FGR.5: Functions & Graphical Models (Georgia Mathematics standard)"
code: 8.FGR.5
cite_as: Georgia Standards of Excellence, Mathematics, 8.FGR.5
subject: math
grades:
  - grade-8
language: en
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source_last_changed: 2024-10-09
data_built: 2026-09-18
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up: https://georgiahomeroom.org/standards/math/grade-8.md
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---

# 8.FGR.5: Functions & Graphical Models

Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.

- Subject: Mathematics
- Appears in: Grade 8, https://georgiahomeroom.org/standards/math/grade-8.md

## Expectations

- **8.FGR.5.1**: Show and explain that a function is a rule that assigns to each input exactly one output.
- **8.FGR.5.2**: Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
- **8.FGR.5.3**: Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
- **8.FGR.5.4**: Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
- **8.FGR.5.5**: Write and explain the equations $y = mx + b$ (slope-intercept form), $Ax + By = C$ (standard form), and $(y - y_1) = m(x - x_1)$ (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
- **8.FGR.5.6**: Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- **8.FGR.5.7**: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two $(x, y)$ values, including reading these from a table or from a graph.
- **8.FGR.5.8**: Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
- **8.FGR.5.9**: Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.

## Georgia Milestones coverage

- Mathematics Grade 8 (EOG). Functional & Graphical Reasoning. Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena. (about 17% of the test; 10 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**: Know the meaning of the domain of a function. Determine the initial value and rate of change of a function. Identify an equation written in one of the three forms as a linear function. Determine the rate of change when given a relationship.
- **Developing**: Recognize whether a relationship is a function. Identify and describe functions based on qualitative features (e.g., linear or nonlinear, increasing or decreasing). Identify the domain of a function when given a table or graphic representation. Compare the initial values and rates of change of two functions represented in the same way. Given specific information, write a linear equation in any form. Determine the initial value when given a table or graph. Given a linear equation in any form, graph the function on a coordinate grid.
- **Proficient**: Explain how a function rule assigns each input to exactly one output. Create and interpret graphs of linear and nonlinear functions that exhibit qualitative features based on realistic situations. Relate the domain of a function to the given real-world or mathematical context. Compare the initial values and rates of change of two functions represented in different ways. Rewrite linear equations in a different form. Explain when to use each form of an equation. Construct linear functions to model relationships in realistic mathematical problems or from a pair of (x, y) values. Explain the meaning of the rate of change and initial value of a linear function in terms of the situation the function models and in terms of its graph or a table of values. Analyze and explain the key characteristics of the graph of a linear function.
- **Distinguished**: Construct, graph, and analyze linear and nonlinear functions; solve realistic problems and interpret functions in terms of the situations they model; and explain key features of linear functions written in various algebraic forms to describe applicable situations.

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