About This Chapter
Understanding & Solving Functions - Chapter Summary
This engaging chapter is designed to improve your understanding of functions and how they are solved. Watch our fun videos to get reacquainted with quadratic, exponential and linear functions, among others. Also, study how function properties are compared numerically and ways specific types of functions are solved. By the end of this chapter, you should be able to:
- Differentiate between relations and functions
- Define and describe a function
- Compare properties of functions numerically, algebraically and graphically
- Share the definition and examples of linear and quadratic functions
- Provide the meaning of an exponential function
- Discuss the properties of polynomial function and basics of factoring
- Use the equation for rational functions
- Give the definition and examples of absolute value functions
Review the lessons in this chapter as short videos that average 8 minutes each or full transcripts you can read online or print to study at a later time. As you navigate the lessons, feel free to submit any questions you have about topics covered. Before taking your test, be sure to find out how well you understand and are ready to solve functions by taking our practice quizzes and exam. These resources are available 24 hours a day and can be accessed used any computer, smartphone or tablet, making your study process simple and effective!
1. The Difference Between Relations & Functions
Relations and functions are a huge part of mathematics. In this lesson, we will define relations and functions. We will look at the differences between the two and how to determine whether a given relation is a function.
2. What is a Function: Basics and Key Terms
Mapping numbers sounds complex, but we do it when we buy gasoline. We pump gasoline, and the gas station charges us based on the amount of gas that we pump. Learn how this relates to functions while reviewing the basics and notations in this lesson.
3. Compare Properties of Functions Numerically
Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.
4. Compare Properties of Functions Algebraically
In this lesson, we will explore algebraic and numeric properties and the evaluation of functions. We'll demonstrate function evaluations and the idea that every element of the domain has a unique element in the range.
5. Compare Properties of Functions Graphically
In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.
6. What is a Linear Function? - Definition & Examples
In this lesson, you will learn the key identifying mark of linear functions. You'll also learn how to graph them with just two points and how you can use the graph to easily find your answers.
7. Quadratic Functions: Examples & Formula
Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.
8. What Is an Exponential Function?
Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!
9. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
10. Rational Function: Definition, Equation & Examples
Rational functions are an extremely useful type of function found in mathematics. They are functions that are fractions whose numerator and denominator are both polynomials. Learn all about them in this lesson!
11. Absolute Value Function: Definition & Examples
The absolute value function shows up in the world around us in many different areas. In this lesson, we will define the absolute value function, look at its characteristics, observe its graph, and look at some examples involving this function.
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