# Ch 21: ORELA Math: Functions

### About This Chapter

## ORELA Math: Functions - Chapter Summary

Review the procedures necessary to solve equations with functions in case you've forgotten some of the fundamental concepts. Explore the key terms and definitions that will help you address related questions on the ORELA Math examination. Go over the rules for composing and compounding functions. Watch these online videos for help with:

- Visualizing functions and identifying graphs of functions
- Transforming functions
- Understanding domain and range of functions and composite functions
- Performing addition, subtraction, multiplication and division operations on functions
- Explaining function notation and composition
- Describing the process of graphing a function of a function
- Confirming, graphing and writing inverse functions
- Creating symmetry and using odd and even functions

Each of the engaging video lessons includes practice problems that you can complete while preparing for the ORELA Math examination. As you study, you may ask questions of the knowledgeable lesson instructors or consult the included text transcripts of the video lessons. Watch the lessons and review functions anywhere. You can test your understanding by taking short self-assessment quizzes as you complete each lesson.

### ORELA Math: Functions Objectives

You'll appreciate having studied the information in this chapter when answering related questions in the Patterns, Algebra and Functions section of the ORELA Math examination. This section amounts to about 24% of the overall score. You should be prepared to answer 150 multiple-choice questions in the allotted four hours and 15 minutes. You can use provided reference materials and an on-screen calculator during the computer-administered examination.

### 1. 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.

### 2. 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.

### 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. Transformations: How to Shift Graphs on a Plane

What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!

### 5. 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.

### 6. 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!

### 7. How to Compose Functions

Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.

### 8. Domain & Range of Composite Functions: Definition & Examples

Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.

### 9. Compounding Functions and Graphing Functions of Functions

We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!

### 10. 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.

### 11. Understanding and Graphing the Inverse Function

If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.

### 12. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis

When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.

### 13. Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin

If you look at flowers and fruits, you'll see that many of these items in nature are symmetrical. In this lesson, learn about symmetry about the origin of a graph. When you are finished, test your knowledge with a short quiz!

### 14. Even & Odd Functions: Definition & Examples

Even and odd functions are an aspect of line symmetry. You can use knowledge of even and odd functions to quickly identify equation symmetry. After this lesson, test your knowledge with a short quiz!

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### Other Chapters

Other chapters within the ORELA Mathematics: Practice & Study Guide course

- ORELA Math: Properties of Real Numbers
- ORELA Math: Fractions
- ORELA Math: Decimals & Percents
- ORELA Math: Ratios & Proportions
- ORELA Math: Units of Measure & Conversions
- ORELA Math: Logic
- ORELA Math: Reasoning
- ORELA Math: Vector Operations
- ORELA Math: Matrix Operations & Determinants
- ORELA Math: Exponents & Exponential Expressions
- ORELA Math: Algebraic Expressions
- ORELA Math: Linear Equations
- ORELA Math: Inequalities
- ORELA Math: Absolute Value
- ORELA Math: Quadratic Equations
- ORELA Math: Polynomials
- ORELA Math: Rational Expressions
- ORELA Math: Radical Expressions
- ORELA Math: Systems of Equations
- ORELA Math: Complex Numbers
- ORELA Math: Piecewise Functions
- ORELA Math: Exponential & Logarithmic Functions
- ORELA Math: Continuity of a Function
- ORELA Math: Limits
- ORELA Math: Rate of Change
- ORELA Math: Calculating Derivatives & Derivative Rules
- ORELA Math: Graphing Derivatives
- ORELA Math: Applications of Derivatives
- ORELA Math: Area Under the Curve & Integrals
- ORELA Math: Integration Techniques
- ORELA Math: Applications of Integration
- ORELA Math: Foundations of Geometry
- ORELA Math: Geometric Figures
- ORELA Math: Properties of Triangles
- ORELA Math: Triangle Theorems & Proofs
- ORELA Math: Parallel Lines & Polygons
- ORELA Math: Quadrilaterals
- ORELA Math: Circles & Arc of a Circle
- ORELA Math: Conic Sections
- ORELA Math: Geometric Solids
- ORELA Math: Analytical Geometry
- ORELA Math: Trigonometric Functions
- ORELA Math: Trigonometric Graphs
- ORELA Math: Solving Trigonometric Equations
- ORELA Math: Trigonometric Identities
- ORELA Math: Sequences & Series
- ORELA Math: Graph Theory
- ORELA Math: Set Theory
- ORELA Math: Statistics Overview
- ORELA Math: Summarizing Data
- ORELA Math: Tables, Plots & Graphs
- ORELA Math: Probability
- ORELA Math: Discrete Probability Distributions
- ORELA Math: Continuous Probability Distributions
- ORELA Math: Sampling
- ORELA Math: Regression & Correlation
- ORELA Mathematics Flashcards