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Honors Algebra 2: Algebraic, Exponential & Log Functions

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Honors Algebra 2: Algebraic, Exponential & Log Functions

This course is part of Honors Algebra 2 Specialization

Instructor: Joseph W. Cutrone, PhD

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4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

No prior experience required

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

Beginner level

No prior experience required

2 weeks to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

16 assignments

Taught in English

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This course is part of the Honors Algebra 2 Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

This is the third course in the Honors Algebra 2 sequence. By the end of this course, students will be able to analyze, interpret, and apply advanced families of functions, including exponential, logarithmic, radical, and inverse functions. Learners will develop fluency in evaluating and graphing these functions, solving equations that involve them, and applying their properties to real-world models and predictions. Along the way, students will deepen their understanding of how different function types connect, building a stronger algebraic foundation for future courses in precalculus, calculus, and beyond.

This course is designed not only to strengthen core problem-solving skills but also to highlight the power of mathematics as a tool for describing patterns and solving practical problems. What makes this course unique is its balance between theory and application: students gain a clear understanding of the underlying algebraic rules while also engaging with meaningful contexts such as growth and decay, investment modeling, and data analysis. By completing this course, learners will be prepared to tackle higher-level mathematics with confidence and insight.

Module details

In earlier courses, you studied polynomials—functions built from whole-number powers of variables. In this module, we expand that perspective to functions with fractional powers, which represent nth roots and can also be written as radical expressions. Our focus will be on building a strong foundation in evaluating radical functions, graphing their behavior, and solving equations that involve them.

What's included

1 video4 readings4 assignments

1 videoTotal 18 minutes

Square Roots and Other Roots18 minutes

4 readingsTotal 35 minutes

The nth Root of a Number5 minutes
Operations with Roots10 minutes
Radical Functions and Graphs10 minutes
Radical Equations and Inequalities10 minutes

4 assignmentsTotal 120 minutes

Radical Functions30 minutes
The nth Root of a Number30 minutes
Graphing Radical Functions30 minutes
Radical Equations and Inequalities30 minutes

We’ve already practiced creating new functions by translating and stretching the graphs of parent functions. In this module, we’ll explore even more ways to build new functions from existing ones. We'll begin by looking at how two functions can be combined to create a new one. Then, we’ll move on to explore inverse functions. Throughout the rest of the course, we’ll keep using these ideas to understand and work with different types of functions.

What's included

2 videos2 readings3 assignments

In this module, we explore two new types of functions that arise when modeling natural phenomena: exponential and logarithmic functions. For example, exponential functions are used to represent the growth of a population, the value of an investment, and the elimination of a drug from the body. Logarithmic functions are the inverses of exponential functions. We will start by examining the key features of these functions and their graphs, then look at algebraic rules to transform and solve equations with them. Finally, we will apply exponential and logarithmic functions to build models and make predictions.

What's included

5 videos4 readings5 assignments

5 videosTotal 97 minutes

Exponential Functions22 minutes
Logarithmic Functions15 minutes
Properties of Logarithms21 minutes
Examples of Exponential Modeling23 minutes
Modeling with Data: Population Growth17 minutes

4 readingsTotal 40 minutes

Exponential Functions5 minutes
Logarithmic Functions10 minutes
Exponential and Logarithmic Equations15 minutes
Modeling with Exponents and Logarithms10 minutes

5 assignmentsTotal 220 minutes

Exponential and Logarithmic Functions60 minutes
Exponential Functions40 minutes
Logarithmic Functions50 minutes
Exponential and Logarithmic Equations30 minutes
Modeling with Exponents and Logarithms40 minutes

For the last module of this course, we will explore rational functions, which arise naturally when modeling inverse variation. These functions are defined as quotients of polynomials. We will learn about the domain, range, and graphs of rational functions, and practice manipulating them with algebra. Finally, we will see how to solve rational equations.