# Ch 14: ACT Math - Functions: Tutoring Solution

### About This Chapter

## How it works:

- Begin your review or other functions work.
- Identify the functions concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our ACT math - functions tutoring solution will benefit any student who is trying to learn functions and earn acceptable scores. This resource can help students including those who:

- Struggle with understanding inverse functions, composition of functions, graphing functions, or any other functions topic
- Have limited time for studying
- Want a cost effective way to supplement their ACT preparation
- Prefer learning ACT topics visually
- Find themselves struggling with the functions portion of the review
- Cope with ADD or ADHD
- Want to get ahead in their functions preparation
- Don't have access to ACT review materials

## Why it works:

**Engaging Tutors:**We make learning about functions simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live ACT prep tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Complete your functions review on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning objectives:

- Review what a function is.
- Learn to write, find and graph inverse functions.
- Find out how to apply various properties of functions to solve complex problems.
- Learn to add, subtract, multiply and divide functions.
- Identify domains and ranges in functions.
- Find out how to compound functions and graph functions of functions.
- Review factoring, polynomials and quadratic functions.
- Learn to simplify problems with exponents.

### 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. Polynomial 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. Polynomial 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.

### 12. Explicit Functions: Definition & Examples

After completing this lesson, you will be able to describe different types of explicit functions. You will also be able to write an explicit function and use it to evaluate values of the input variable.

### 13. Function Operation: Definition & Overview

In this lesson, we will define functions and determine how to use specific rules for the addition, subtraction, multiplication, and division of functions.

### 14. Function Table in Math: Definition, Rules & Examples

Functions can be represented in four different ways. In this lesson, we will learn what a function table is, and how and when to use a function table to represent a function. We will also explore the rules that define a given function table.

### 15. Hyperbolic Functions: Properties & Applications

Although related to trigonometric functions, hyperbolic functions have special properties. In this lesson, you'll explore the properties of hyperbolic functions and their usage in both theoretical and real-world applications.

### 16. Increasing Function: Definition & Example

In this lesson, we will learn what it means for a function to be increasing. We will also learn how to determine if a given function is increasing by observing its graph and working with its derivative.

### 17. Parent Function in Math: Definition & Examples

This lesson will familiarize us with parent functions. We will look at many examples to learn the definitions of both families of functions and parent functions. We will also look at identifying a parent function in a family of functions.

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### Other Chapters

Other chapters within the ACT Prep: Tutoring Solution course

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