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
Linear functions are first-degree functions that form a straight line when graphed; these functions have one or two variables and no exponents or powers. Discover the characteristics of a linear function, and learn how to graph a linear function using two or more points.
3. Logarithmic Function: Definition & Examples
Exponential functions and logarithmic functions are closely tied. In fact, they are so closely tied we could say a logarithm is actually an exponent in disguise. A logarithm, or log, is just another way to write an exponential function in reverse.
4. What Is an Exponential Function?
Exponential functions are written as y = ab^x. Examine what exponential functions are in this lesson and learn how these functions can be illustrated using graphs.
5. Using Linear & Exponential Functions to Model Situations
Linear and exponential functions can both be used to model data. In this lesson, learn about these two important functions and how and when to use each one.
6. Modeling with Exponential & Logarithmic Functions
This lesson will give a quick review of exponential and logarithmic functions and when to use these functions to model data. Then we will explore the use of graphing calculators in finding exponential and logarithmic functions to model given data.
7. Quadratic Functions: Examples & Formula
Quadratic functions are mathematical expressions where the highest power is two. Study the definition of quadratic function and how they look on a graph. See examples of how to write a quadratic in three different forms, and the learn the quadratic formula.
8. 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.
9. Polynomial Functions: Properties and Factoring
Polynomial functions are those in which multiple terms are added together. Explore quadratic polynomials and discover why they are easy to work with since they can be factored, and solved, with the quadratic equation.
10. Polynomial Functions: Exponentials and Simplifying
Repeated multiplications can be written as x^n, where x is multiplied by itself n times. Explore multiplication, division, and power properties of polynomials functions, as well as exponentials and simplifying using the bunny problem as an example.
11. 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.
12. 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.
13. What is a Radical Function? - Definition, Equations & Graphs
Radical functions operate very differently than regular functions. This lesson covers the definitions, equations, and graphs that you will need to know to be successful with radical functions.
14. What are Piecewise Functions?
Piecewise functions in math are known to be made up of multiple parts and help calculate rates and other math problems. Discover what a function is, specific types of mathematical functions, how to evaluate piecewise functions, and some real world examples.
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