# Ch 3: Explorations in Core Math Algebra 1 Chapter 3: Functions

### About This Chapter

## How It Works:

- Identify the lessons in the Explorations in Core Math Algebra 1 chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the 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:

- Constructing graphs and interpretation
- Line graphs
- Identifying functions
- Domain and range
- Plotting points
- Linear and nonlinear functions
- Arithmetic with functions
- Inverse functions
- Graphing piecewise functions
- Examples of step functions
- Scatterplot and correlation
- Line of best fit
- Evaluating real-life linear models
- Finding and classifying an arithmetic sequence
- Using recursive rules

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. How to Construct Graphs from Data & Interpret Them

After watching this video, you should be able to explain what a graph is, construct a scatter plot, and interpret scatter plots from scientific data. A short quiz will follow.

### 2. Reading and Interpreting Line Graphs

Watch this video lesson to find out how useful line graphs can be and how much information you can gain just from looking at one. Learn how you can apply that information in your own life to help you make better decisions.

### 3. 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!

### 4. What Is Domain and Range in a Function?

The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.

### 5. 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.

### 6. Linear and Nonlinear Functions

After watching this video lesson, you'll be able to tell the differences between linear and nonlinear functions. You'll also be able to identify both types just by looking at graphs.

### 7. How to Add, Subtract, Multiply and Divide Functions

Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!

### 8. Inverse Functions

Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.

### 9. How to Graph Piecewise Functions

Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.

### 10. Step Function: Definition, Equation & Examples

In this lesson, we'll learn what a step function is and become comfortable with this type of function. We'll examine common examples, such as the floor and ceiling functions and the heaviside function.

### 11. Scatterplot and Correlation: Definition, Example & Analysis

A scatterplot is used to graphically represent the relationship between two variables. Explore the relationship between scatterplots and correlations, the different types of correlations, how to interpret scatterplots, and more.

### 12. Line of Best Fit: Definition, Equation & Examples

Linear graphs are a terrific way to see a trend when comparing any two factors. A line of best fit is the trendline that best fits the data set. In this lesson, we will see how the line of best fit helps to predict future events.

### 13. Writing & Evaluating Real-Life Linear Models: Process & Examples

You make decisions about budgeting and other financial issues using linear models without even realizing it. Learn how to write and evaluate linear models.

### 14. 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!

### 15. Using Recursive Rules for Arithmetic, Algebraic & Geometric Sequences

When dealing with sequences in math, both algebraic and geometric, we come across recursive rules. Watch this video lesson to learn how recursion works and how you can use a recursive rule to get to your next number using a previous number.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 1: Equations
- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 4: Linear Functions
- Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities
- Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis