About This Chapter
Characteristics & Relationships of Functions - Chapter Summary
Our instructors outline the characteristics and relationships of functions in this informative chapter. You'll study the difference between functions and relations, as well as the algebraic function. After completing this chapter, you should be ready to:
- Calculate outputs and inputs of functions
- Detail linear functions with examples
- Understand how the slope and intercept of a linear model is interpreted
- Explain nonlinear functions and provide examples
- Identify intercepts for nonlinear functions
- Describe how families of functions are identified
- Compare the properties of functions graphically, numerically and algebraically
- Outline the functional correlation between quantities
We've made it convenient for you study whenever you'd like by making these learning tools accessible 24 hours a day on your mobile device or computer. Our video lessons are generally less than 10 minutes long, easy to navigate and accompanied by short quizzes to help check your comprehension. As you move through the chapter, you can track your progress in the Dashboard. Any questions you might have along the way can be directed to one of our instructors to answer.
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. Algebraic Function: Definition & Examples
An algebraic function is a type of equation that uses mathematical operations. An equation is a function if there is a one-to-one relationship between its x-values and y-values.
3. Determining Inputs & Outputs of Functions
Functions are like the manufacturing plants of mathematics: One thing goes in, another comes out. In this lesson, we'll discuss how to determine the inputs and outputs of functions that show up as tables, graphs, or algebraic expressions.
4. 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.
5. Interpreting the Slope & Intercept of a Linear Model
You've probably seen slope and intercept in algebra. These concepts can also be used to predict and understand information in statistics. Take a look at this lesson!
6. Nonlinear Function: Definition & Examples
In this lesson, we will familiarize ourselves with linear functions in order to define and understand what nonlinear functions are. We will become comfortable determining if a function is linear or nonlinear through definitions and examples.
7. Determining Intercepts for Nonlinear Functions
This lesson will define linear and nonlinear functions. We will then go on to explore the intercepts of nonlinear functions and look at how to identify them graphically and algebraically using a real-world example.
8. How to Identify Families of Functions
Functions come in all kinds of varieties, but they can be grouped together into families that have common characteristics. The difference and similarities can be seen in the equations and graphs of these functions. In this lesson, you will learn about the characteristics of different families of functions and how to recognize them based on their equations and graphs.
9. 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.
10. 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.
11. 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.
12. Describe the Functional Relationship Between Quantities
In this lesson, you'll learn how to look at a graph, table, or function written mathematically and verbally describe the functional relationship shown. For example, you'll learn to describe whether the function is increasing or decreasing.
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Other chapters within the GACE Special Education Mathematics & Science (088): Practice & Study Guide course
- Working with Real Numbers
- Fractions, Decimals, Percents & Ratios
- Understanding Number Theory & Estimation
- Overview of Basic Algebra
- Patterns & Sequences in Algebra
- Solving Basic Geometric Problems
- Points, Lines, Rays & Angles
- Solving Angle Problems with Triangles & Quadrilaterals
- Geometric Relationships in the Coordinate Plane
- Solving Problems Involving Systems of Measurement
- Displaying & Interpreting Data
- Measures of Central Tendency
- Statistical Models & Processes
- Understanding Probability, Combinations & Permutations
- Scientific Inquiry & Design
- Nature of Scientific Knowledge
- Major Developments & Historical Figures in Science
- Collecting & Evaluating Scientific Data
- Science Laboratory & Field Equipment Safety
- Environmental Effects of Science & Technology
- Energy Production & Natural Resource Management
- Science & Technology in Consumer Products
- Atoms, Energy & Matter
- Concepts & Relationships Between Energy & Matter
- Basics of the Periodic Table
- Chemical Compounds & Reactions
- Acid-Base Chemistry
- Solutions & Solubility
- Concepts of Mechanics Overview
- Electricity & Magnetism Overview
- Waves & Optics Overview
- Structure & Function of Cells & Organelles
- Basic Biochemistry of Life
- Basic Genetics
- Evolution, Natural Selection & Biological Diversity
- Hierarchical Classification of Living Things
- Understanding Plant Structures & Function
- Animal & Human Anatomy & Physiology
- Population Dynamics & Ecology
- Rocks, Minerals & Soil Overview
- Earth's Structure, Shape & Processes
- Historical Geology
- Understanding the Earth's Oceans
- Freshwater Characteristics & Processes
- Atmosphere & Weather
- Climate, Seasons & Geography
- Exploring Features of the Solar System
- Earth-Moon-Sun System
- GACE Special Education Mathematics & Science Flashcards