Exponential Functions Unit | Growth, Decay, Asymptotes & Transformations

Description

Teach exponential functions with this complete unit covering growth, decay, asymptotes, transformations, tables, graphs, equations, and real-world models. Students build understanding through clear explanations, multi-representation tasks, hands-on activities, warm-ups, and five versions of an assessment.

This unit supports Algebra 2 instruction by addressing key exponential concepts introduced in Algebra 1 and extending them through transformations, modeling, and preparation for logarithmic functions.

This unit includes a teacher roadmap, built-in pause points, and math starters for flexible pacing, warm-ups, and exit tickets.

This Exponential Functions Unit takes students through every major concept in exponential functions using a mix of short explanations, multi-representation tasks, and real-world problems. Students explore growth and decay, y-intercepts, asymptotes, inverse relationships, and transformations using tables, graphs, equations, and modeling situations. The pages can be used in sequence for a full unit or assigned individually for differentiation, review, or intervention.

Students begin with a quick exponents review and then move into identifying growth vs. decay, completing tables, building equations from patterns, and graphing functions to determine key features. They compare functions side-by-side, justify statements, and analyze how parameters affect the shape of the graph.

The unit includes real-world applications such as half-life, compound interest (including continuous compounding using e), population modeling, and house-value appreciation and depreciation. A paper-folding activity allows students to collect data and observe exponential change in a hands-on, visual way.

Transformations appear naturally as students compare functions and identify vertical/horizontal shifts, reflections, and stretches/compressions. Students practice matching graphs to functions and writing new functions using the form f(x) = a·b^(x – h) + k.

What’s Included

• Exponents review (fill-in-the-blank)
• Growth vs. decay explanation
• Multi-representation tasks (tables, graphs, equations)
• Y-intercepts, asymptotes, and inverse table creation
• Graphing exponential functions and identifying domain, range, y-intercept, and asymptote
• Build exponential equations from tables
• Growth/decay models (population, house values, percent change)
• Half-life real-world problem
• Paper-folding activity (collect data → table → graph → analysis)
• Compound interest and continuous compounding using A = Pe^rt
• Transformations of exponential functions
• Matching graphs to functions
• Describe transformations from the parent function
• Write transformed functions using f(x) = a·b^(x – h) + k
• 5 different assessment versions (A–E)
• 10 Math Starters (Warm-ups)
• Answer keys included

How to Use This Unit

Designed for Algebra 2:

This unit is written with Algebra 2 classrooms in mind. It provides targeted prerequisite review of exponential concepts and then moves students into core Algebra 2 instruction, including transformations, asymptotes, inverse thinking, continuous compounding, and deeper real-world modeling. Teachers use this unit as a bridge into logarithmic functions.

****Here's the next unit: Log Functions Unit

Adaptation for Algebra 1 (optional):

Select portions of the unit can be used in Algebra 1, including growth and decay modeling, graphing practice, table–equation–graph conversions, real-world problems, paper-folding activities, half-life, and introductory transformations. Advanced transformation work and continuous compounding can be shortened or omitted as needed.

Perfect For

• Algebra 2 instruction and review of exponential functions
• Targeted prerequisite recovery of Algebra 1 exponential concepts
• Teaching transformations, asymptotes, and exponential modeling
• Real-world modeling lessons and applications
• Pre-AP / honors Algebra 2 extensions
• Small-group instruction or intervention
• Review before an assessment
• Test-prep warm-ups (STAAR, TSI, PSAT/SAT/ACT)

Copyright ©Time Flies/Lisa Hamiter. All rights reserved by author. This product is to be used by the original downloader only. Copying for more than one teacher, classroom or school system is prohibited.