About This Chapter
ACT Math: Types of Functions - Chapter Summary
If you need to study for the ACT Math section, work through this chapter to review different types of functions and practice solving function problems. The chapter provides short and engaging lessons that show you how to work with a variety of functions, including linear, polynomial, recursive and quadratic functions. Upon completion of the chapter, you should be able to:
- Recognize composite, linear, exponential, quadratic and recursive functions
- Evaluate exponential and linear modeling from real-world scenarios
- Model with quadratic and polynomial functions
- Factor and simplify polynomial functions
- Use the recursive sequence formula
When you finish a lesson, you can make sure you fully understand the material by taking the accompanying self-assessment quiz. Take the chapter exam to practice applying your math skills. If you have any questions about the material, you can reach out to our subject-matter experts online.
1. Composite Function: Definition & Examples
One way in which we can combine functions is by forming their composition. A composite function is a larger function that is created by putting one function inside another function.
2. What is a Linear Function? - Definition & Examples
In this lesson, you will learn the key identifying mark of linear functions. You'll also learn how to graph them with just two points and how you can use the graph to easily find your answers.
3. What Is an Exponential Function?
Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!
4. Linear & Exponential Modeling from Real World Situations
In this lesson, we will start with an example of using linear and exponential models in a real-world situation. We will then explore these models and discuss how to know which model to use in a scenario, based on a phenomenon's rate of change.
5. Quadratic Functions: Examples & Formula
Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.
6. Modeling with Quadratic Functions
In this lesson, you will learn how to use a quadratic function in the standard, vertex, and factored forms to model a real-life scenario. You will describe and evaluate a path of a launched object using quadratic modeling.
7. 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.
8. 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.
9. Modeling with Polynomial Functions
Modeling real-world phenomena with a function is an extremely useful tool to have at our disposal. This lesson will explain how to model a given set of data points with polynomial functions using the method of finite differences.
10. Recursive Functions: Definition & Examples
After reading this lesson, you'll know how to identify recursive functions and how they work. You'll learn how to figure out the terms of these recursive functions, and you'll learn about a famous recursive function.
11. Recursive Sequence: Formula & Overview
One of the most famous recursive sequences is the Fibonacci sequence. In this lesson, learn what makes the Fibonacci sequence a recursive sequence, and discover how you can recognize and create your own.
12. What are Piecewise Functions?
A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.
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