# Ch 14: ACT Math: Functions

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### About This Chapter

## ACT Math: Functions - Chapter Summary

Our lessons define functions and review the basic, key terms. You'll look at the following topics:

- Composing functions
- Working with functions: adding, subtracting, multiplying and dividing
- Range and domain
- Compounding and graphing
- Inverse functions
- Polynomials: properties, factoring, exponentials and simplifying

In addition to the motivating videos and quizzes for self-assessment, this chapter also guides you through practice problems in the identification, application and notation of function operations.

### ACT Math Objectives

The ACT assesses your math skills through a 60-minute exam with 60 multiple-choice questions. You won't need to know complicated formulas, but the test does assume an understanding of basic computational skills and fundamental formulas. The test covers six content areas:

- Pre-algebra
- Elementary algebra
- Intermediate algebra
- Coordinate geometry
- Plane geometry
- Trigonometry

The elementary algebra portion comprises 17% of the test questions and includes the following areas:

- Properties of exponents
- Using variables to express functional relationships
- Understanding algebraic operations

The part of the test that addresses intermediate algebra topics constitutes 15% of the exam and involves the topics below:

- Functions
- Modeling
- Polynomials

You'll receive four math scores, including an overall score for all of the questions and sub-scores for pre-algebra/elementary algebra, intermediate algebra/coordinate geometry and plane geometry/trigonometry.

The lessons in this chapter will assist your review of functions for the ACT. Start with the basics, and then work on applying, composing, compounding and graphing functions. Complete the problems in identification and notation for extra practice.

### 1. 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.

### 2. 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.

### 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. 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.

### 5. 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!

### 6. 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.

### 7. 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!

### 8. 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!

### 9. 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.

### 10. Polynomials Functions: Properties and Factoring

Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.

### 11. Polynomials Functions: Exponentials and Simplifying

How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.

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### Other Chapters

Other chapters within the ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Inequalities
- ACT Math: Probability, Combinations & Factorial
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Complex Numbers
- ACT Math: Exponentials and Logarithms
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Plane Geometry
- ACT Math: Logic in Mathematics
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Literary Terms
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Parts of an Essay
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills