# Ch 21: OAE Mathematics: Functions

### About This Chapter

## OAE Mathematics: Functions - Chapter Summary

Use this chapter to help you review the algebraic, graphical, and numerical properties of functions before taking the OAE Mathematics exam. It also explores the mathematical manipulation of these same properties, whether it be graphical transformations or adding and subtracting functions. By the end of the chapter you will have reviewed:

- Comparing function's algebraic, graphical, numerical properties
- Graphical transformations of functions
- Identifying the domain and range of a function
- Composing functions
- Adding, subtracting, multiplying, and dividing functions
- Composing functions
- Examples of the domain and range of composite functions
- Inverse functions
- The symmetry of functions
- Recognizing even and odd functions

Each exciting video lesson features a series of practice questions. These questions are based on those you could see o- your upcoming exam. The test is only 3 hours and 45 minutes so it is important to be familiar with the question types you will soon face.

### Objectives of the OAE Mathematics: Functions Chapter

The OAE Math exam is a computer based test assessing teacher's knowledge of five domains. This function chapter links to questions you may find in the patterns, algebra, and functions section of the OAE Mathematics exam. The section comprises about 24% of the 150 multiple-choice question.

### 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 Ohio Assessments for Educators - Mathematics (027): Practice & Study Guide course

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