# Ch 33: Compass Math: Function Operations

### About This Chapter

## Compass Math: Function Operations - Chapter Summary

The chapter's lessons will get you well-acquainted with different function types and how to perform various function operations. The lessons contain a number of clear, effective examples. The quizzes throughout this chapter give you practice with the following Compass Math test prep content:

- Composition of functions
- Solving one-to-one functions
- Adding, subtracting, multiplying and dividing functions
- Compounding functions
- Graphing functions of functions
- Manipulating functions and
- Solving equations for differing variables
- Composite functions: domain and range
- Writing and finding inverse functions

Our professional instructors take you through these function topics one by one in the short, engaging video lessons. In addition to the many key terms in this chapter, there will be some information about related courses that you can study.

### Objectives of the Compass Math: Function Operations Chapter

Compass Math test performance can be used to help with scheduling the most suitable courses for you based on your abilities. There are five parts to the math exam, and the Compass Math College Algebra Placement Test features content involving functions. All of the questions that you answer on the test concerning content in this chapter will be in multiple-choice format.

### 1. 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!

### 2. 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.

### 3. Applying Function Operations Practice Problems

In this lesson, learn how to apply all the different properties of functions to solve complex problems. From function operations and composition to domain and range, get your practice here!

### 4. 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!

### 5. 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.

### 6. 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.

### 7. 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.

### 8. One-to-One Functions: Definitions and Examples

Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.

### 9. Manipulating Functions and Solving Equations for Different Variables

Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.

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### Other Chapters

Other chapters within the ACT Compass Math Test: Practice & Study Guide course

- Compass Math: Integers
- Compass Math: Decimals
- Compass Math: Fractions
- Compass Math: Exponents
- Compass Math: Roots & Radicals
- Compass Math: Percents
- Compass Math: Ratios, Rates & Proportions
- Compass Math: Median, Mean & Mode
- Compass Math: Algebraic Equations & Expressions
- Compass Math: Linear Equations
- Compass Math: Substituting Values
- Compass Math: Monomials & Polynomials
- Compass Math: Factoring Polynomials
- Compass Math: Matrices & Absolute Value
- Compass Math: Inequalities
- Compass Math: Complex Numbers
- Compass Math: Logarithms
- Compass Math: Basic Geometry
- Compass Math: Lines & Angles
- Compass Math: Polygons
- Compass Math: Triangles
- Compass Math: Quadrilaterals
- Compass Math: Circles
- Compass Math: Similar Figures
- Compass Math: Complex Figures
- Compass Math: Constructions
- Compass Math: Area, Circumference & Perimeter
- Compass Math: Mathematical Modeling
- Compass Math: Quadratics
- Compass Math: Quadratic Functions
- Compass Math: Trigonometric Functions
- Compass Math: Rational Functions
- Compass Math: Trigonometric Identities
- Compass Math: Trigonometric Equations
- Compass Math: Trigonometric Applications
- Compass Math: Trigonometric Graphs
- Compass Math: Graph Symmetry
- Compass Math: Polar Coordinates & Parameterization