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Algebra: Elementary to Advanced - Functions & Applications

Algebra: Elementary to Advanced - Functions & Applications

This course is part of Algebra: Elementary to Advanced Specialization

Instructor: Joseph W. Cutrone, PhD

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3 modules

Gain insight into a topic and learn the fundamentals.

197 reviews

Beginner level

No prior experience required

6 hours to complete

Flexible schedule

Learn at your own pace

3 modules

Gain insight into a topic and learn the fundamentals.

197 reviews

Beginner level

No prior experience required

6 hours to complete

Flexible schedule

Learn at your own pace

Skills you'll gain

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

5 assignments

Taught in English

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This course is part of the Algebra: Elementary to Advanced Specialization

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There are 3 modules in this course

After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition. These functions are then applied to solve real world problems. The ability to picture many different types of functions will help students learn how and when to apply these functions, as well as give students the geometric intuition to understand the algebraic techniques. The skills and objectives from this course improve problem solving abilities.

Module details

A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear functions have the property that any chance in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modeled using a linear relationship. Adding an extra term of the form ax^2 to a linear function creates a quadratic function, and its graph is the parabola. We will see examples of linear and quadratic functions and their applications in the sections that follow.

What's included

2 videos5 readings2 assignments

2 videosTotal 40 minutes

Linear Functions20 minutes
Quadratic Functions20 minutes

5 readingsTotal 50 minutes

Notes: Linear Functions10 minutes
Transforming Graphs of Functions10 minutes
Sample Problems: Linear Functions10 minutes
Notes: Quadratic Functions10 minutes
Sample Problems: Quadratic Functions10 minutes

2 assignmentsTotal 60 minutes

Linear Functions30 minutes
Quadratic Functions30 minutes

In the last module we introduced the important concept of a function and considered the linear and quadratic functions. In this module, we discuss methods for building new functions from those that are already familiar to use. One method will use the graph shifting techniques already introduced. These methods are developed further and applied to new functions. Constructing a graph is often an important first step in solving a problem. The more functions you can picture, the better problem solver you will be.

What's included

3 videos5 readings2 assignments

3 videosTotal 52 minutes

Common Functions23 minutes
Less Common Functions17 minutes
Function Composition13 minutes

5 readingsTotal 50 minutes

Notes: A Collection of Functions10 minutes
Notes: Combinations of Functions10 minutes
Sample Problems: Modeling Functions10 minutes
Notes: Applications of Functions10 minutes
Sample Problems: Applications of Functions10 minutes

2 assignmentsTotal 60 minutes

Modeling Functions30 minutes
Applications of Functions30 minutes

Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!