---
title: "A.FGR.9: Exponential Function Graphs (Georgia Mathematics standard)"
code: A.FGR.9
cite_as: Georgia Standards of Excellence, Mathematics, A.FGR.9
subject: math
grades:
  - high-school
language: en
canonical_url: https://georgiahomeroom.org/standards/code/A.FGR.9
md_url: https://georgiahomeroom.org/standards/code/A.FGR.9.md
alternate_language_url: https://georgiahomeroom.org/es/standards/code/A.FGR.9.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.9: Exponential Function Graphs

Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions.

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

## Expectations

- **A.FGR.9.1**: Use function notation to build and evaluate exponential functions for inputs in their domains and interpret statements that use function notation in terms of a context.
- **A.FGR.9.2**: Graph and analyze the key characteristics of simple exponential functions based on mathematically applicable situations.
- **A.FGR.9.3**: Identify the effect on the graph generated by an exponential function when replacing $f(x)$ with $f(x)$ + $k$, and $k f(x)$, for specific values of $k$ (both positive and negative); find the value of $k$ given the graphs.
- **A.FGR.9.4**: Use mathematically applicable situations algebraically and graphically to build and interpret geometric sequences as functions whose domain is a subset of the integers.
- **A.FGR.9.5**: Compare characteristics of two functions each represented in a different way.

## Georgia Milestones coverage

- Algebra I (EOC). Functional & Graphical Reasoning. Construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions. (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**: Evaluate an exponential function for a specific value of the domain. Identify a term in a geometric sequence.
- **Developing**: Interpret an exponential function for a given value of the domain in context. Given a table of values or a graph representing an exponential function, identify key features of the function. Given the graph of the exponential function f(x), identify the graph of f(x) + k or kf(x). Identify a rule to describe a geometric sequence.
- **Proficient**: Create an exponential function that represents a real-life situation. Create the graph of an exponential function and identify key features from the graph. Explain the result of replacing the exponential function f(x) with f(x) + k or kf(x). Solve real-life problems involving geometric sequences. Compare key features of two functions presented in different ways (e.g., tables, equations, graphs).
- **Distinguished**: Given an exponential function in a real-life situation, explain the impact of adding a constant (i.e., f(x) + k) or multiplying the output by a constant (i.e., kf(x)) within the context of the situation. Solve real-life problems involving functions in various forms and compare the key features in mathematically applicable situations.

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