About This Chapter
NES Math: Functions - Chapter Summary
Let us aid in your preparation for the NES Math test with lessons covering the properties of functions and related operations. Our videos offer reviews of the following:
- Comparison of properties of functions algebraically, graphically and numerically
- How to shift graphs on a plane
- Domain and range in a function
- Addition, subtraction, multiplication and division of functions
- Inverse functions and how to graph them
- Recognizing symmetry graphically, algebraically and numerically about the origin, x-axis and y-axis
- Even and odd functions
You can watch these video lessons on a tablet, phone or computer whenever you have a few minutes to spend on study. After each lesson is a short quiz, so you can immediately assess your knowledge. The answer keys contain links that let you quickly return to the section of the video lesson that discusses questions you answered incorrectly. Other study tools include text transcripts and a Dashboard that helps you keep up with your studies.
NES Math: Functions Chapter Objectives
Five states make passing the NES Math test one of the conditions for obtaining certification to teach the subject at the secondary level. The test's questions are sectioned into five content domains, and the material from this chapter is covered in the Patterns, Algebra, and Functions content domain. This section makes up 24% of the test's total scoring.
All the NES Math test questions are multiple-choice, requiring you to solve a problem or read a question and select the correct answer from several options. The test is computer-based. Answering our quiz and chapter exam questions, which are also multiple-choice, provides experience with the sorts of questions you'll encounter on the NES test.
1. Compare Properties of Functions Algebraically
In this lesson, we will explore algebraic and numeric properties and the evaluation of functions. We'll demonstrate function evaluations and the idea that every element of the domain has a unique element in the range.
2. Compare Properties of Functions Graphically
In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.
3. Compare Properties of Functions Numerically
Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.
4. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
5. 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.
6. 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!
7. 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.
8. 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.
9. 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!
10. 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.
11. 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.
12. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis
When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.
13. Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin
If you look at flowers and fruits, you'll see that many of these items in nature are symmetrical. In this lesson, learn about symmetry about the origin of a graph. When you are finished, test your knowledge with a short quiz!
14. Even & Odd Functions: Definition & Examples
Even and odd functions are an aspect of line symmetry. You can use knowledge of even and odd functions to quickly identify equation symmetry. After this lesson, test your knowledge with a short quiz!
Earning College Credit
Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the NES Mathematics (304): Practice & Study Guide course
- NES Math: Properties of Real Numbers
- NES Math: Fractions
- NES Math: Decimals & Percents
- NES Math: Ratios & Proportions
- NES Math: Units of Measure & Conversions
- NES Math: Logic
- NES Math: Reasoning
- NES Math: Vector Operations
- NES Math: Matrix Operations & Determinants
- NES Math: Exponents & Exponential Expressions
- NES Math: Algebraic Expressions
- NES Math: Linear Equations
- NES Math: Inequalities
- NES Math: Absolute Value
- NES Math: Quadratic Equations
- NES Math: Polynomials
- NES Math: Rational Expressions
- NES Math: Radical Expressions
- NES Math: Systems of Equations
- NES Math: Complex Numbers
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- NES Math: Continuity of Functions
- NES Math: Limits
- NES Math: Rate of Change
- NES Math: Derivative Rules
- NES Math: Graphing Derivatives
- NES Math: Applications of Derivatives
- NES Math: Area Under the Curve & Integrals
- NES Math: Integration Techniques
- NES Math: Applications of Integration
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- NES Math: Properties of Triangles
- NES Math: Triangle Theorems & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Quadrilaterals
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- NES Math: Trigonometric Functions
- NES Math: Trigonometric Graphs
- NES Math: Solving Trigonometric Equations
- NES Math: Trigonometric Identities
- NES Math: Sequences & Series
- NES Math: Graph Theory
- NES Math: Set Theory
- NES Math: Statistics Overview
- NES Math: Summarizing Data
- NES Math: Tables, Plots & Graphs
- NES Math: Probability
- NES Math: Discrete Probability Distributions
- NES Math: Continuous Probability Distributions
- NES Math: Sampling
- NES Math: Regression & Correlation