# Ch 32: HiSET Mathematics: Functions

### About This Chapter

## HiSET Mathematics: Functions - Chapter Summary

Watch the videos in this chapter to see how to use functions as equations. Our expert instructors teach the short video lessons using real-world examples so you can see how these concepts are applied. Use the self-assessment quizzes as another tool to help you review the topics you'll see on the HiSET, such as:

- Comparing properties of functions algebraically, graphically and numerically
- Identifying transformations
- Domain and range in a function
- Adding, subtracting, multiplying and dividing functions
- Composing functions
- Domain and range of composite functions
- Compounding functions and graphing functions of functions
- Graphing the inverse function
- Identifying symmetry graphically, algebraically and numerically about the x-axis, y-axis and origin
- Even and odd functions

### Objectives of the HiSET Mathematics: Functions Chapter

The HiSET Math exam is divided into four sections, and the topics in this Functions chapter will be in the Algebraic Concepts section. This section constitutes 45% of the math test which means of the 50 total questions, about 22 or 23 questions will be on algebra.

All of the questions are multiple-choice, so you will have to choose one correct answer from a list of possible answers.

### 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!

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### Other Chapters

Other chapters within the HiSET Mathematics: Prep and Practice course

- HiSET Mathematics: Mathematical Reasoning
- HiSET Mathematics: Properties of Real Numbers
- HiSET Mathematics: Fractions
- HiSET Mathematics: Decimals and Percents
- HiSET Mathematics: Ratios and Proportions
- HiSET Mathematics: Vector Operations
- HiSET Mathematics: Matrices and Determinants
- HiSET Mathematics: Exponents and Exponential Expressions
- HiSET Mathematics: Absolute Value Problems
- HiSET Mathematics: Rational Expressions
- HiSET Mathematics: Radical Expressions
- HiSET Mathematics: Imaginary and Complex Numbers
- HiSET Mathematics: Measurements and Conversions
- HiSET Mathematics: Foundations of Geometry
- HiSET Mathematics: Introduction to Geometric Figures
- HiSET Mathematics: Properties of Triangles
- HiSET Mathematics: Triangle Theorems and Proofs
- HiSET Mathematics: Parallel Lines and Polygons
- HiSET Mathematics: Quadrilaterals
- HiSET Mathematics: Circular Arcs and Circles
- HiSET Mathematics: Geometric Solids
- HiSET Mathematics: Summarizing Data
- HiSET Mathematics: Probability
- HiSET Mathematics: Probability Distributions
- HiSET Mathematics: Sampling
- HiSET Mathematics: Regression and Correlation
- HiSET Mathematics: Algebraic Expressions
- HiSET Mathematics: Linear Equations
- HiSET Mathematics: Inequalities
- HiSET Mathematics: Quadratic Equations
- HiSET Mathematics: Polynomials
- HiSET Mathematics Flashcards