# Ch 4: Glencoe Algebra 1 Chapter 4: Graphing Relations and Functions

### About This Chapter

## How it works:

- Identify the lessons in the Glencoe Algebra 1 Graphing Relations and Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the graphing relations and functions topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- The coordinate plane and Cartesian coordinate system
- Transformations and translation
- Relations and inverse relations
- Graphs of basic functions and solutions for simple linear equations
- Graphs of linear equations
- Function identification and notation
- Function properties
- Arithmetic sequences
- Deductive and inductive reasoning
- Equation recognition using patterns

*Glencoe is a registered trademark of McGraw-Hill Education, which is not affiliated with Study.com.*

### 1. Plotting Points on the Coordinate Plane

If you'll be working with a graph, otherwise known as the coordinate plane, it's essential to understand how it works. This includes learning the parts of a graph, identifying points and plotting points.

### 2. The Cartesian Coordinate System: Plotting Points & Graphing Lines

Watch this video lesson to see how useful the Cartesian coordinate system is. Learn how points are labeled and how you can plot points and graph lines using the system.

### 3. Transformations in Math: Definition & Graph

In geometry, transformation refers to the movement of objects in the coordinate plane. This lesson will define and give examples of each of the four common transformations and end with a quiz to make sure you are moving in the right direction.

### 4. What is Translation in Math? - Definition, Examples, & Terms

In mathematics, translation refers to moving an object without changing it in any other way. This lesson will describe how to translate an object and give some examples. A quiz will follow to test your knowledge.

### 5. Describing the Relationship between Two Quantitative Variables

In this video lesson, you will learn about quantitative variables, what they are, and how one variable relates to another. You will learn why this is important and why it can sometimes even save lives.

### 6. Graphing Basic Functions

Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.

### 7. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

### 8. 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.

### 9. Functions: Identification, Notation & Practice Problems

A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!

### 10. What is a Function? - Applying the Vertical Line Test

Equations come in all shapes and sizes. Trying to determine which equations are functions can be difficult. You can apply the vertical line test to a graph to quickly tell whether or not it is a function.

### 11. 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.

### 12. 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.

### 13. How to Find and Classify an Arithmetic Sequence

Arithmetic sequences are everywhere, and with a few tricks you learn here, you could end up looking like a psychic the next time you go to a movie or a football game!

### 14. How and Why to Use the General Term of an Arithmetic Sequence

Watch this video lesson to learn the formula for the general term of an arithmetic sequence. Also learn why this formula makes working with an arithmetic sequence much easier.

### 15. Inductive & Deductive Reasoning in Geometry: Definition & Uses

Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.

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### Other Chapters

Other chapters within the Glencoe Algebra 1: Online Textbook Help course

- Glencoe Algebra 1 Chapter 1: The Language of Algebra
- Glencoe Algebra 1 Chapter 2: Real Numbers
- Glencoe Algebra 1 Chapter 3: Solving Linear Equations
- Glencoe Algebra 1 Chapter 5: Analyzing Linear Equations
- Glencoe Algebra 1 Chapter 6: Solving Linear Inequalities
- Glencoe Algebra 1 Chapter 7: Solving Systems of Linear Equations and Inequalities
- Glencoe Algebra 1 Chapter 8: Polynomials
- Glencoe Algebra 1 Chapter 9: Factoring
- Glencoe Algebra 1 Chapter 10: Quadratic and Exponential Functions
- Glencoe Algebra 1 Chapter 11: Radical Expressions and Triangles
- Glencoe Algebra 1 Chapter 12: Rational Expressions and Equations
- Glencoe Algebra 1 Chapter 13: Statistics
- Glencoe Algebra 1 Chapter 14: Probability