About This Chapter
TACHS: Properties of Functions - Chapter Summary
This chapter emphasizes key terms and definitions related to functions. Your student can review how to perform operations with functions and discover different kinds of transformations when going through each of these educational video lessons on the properties of functions. The rules of domain and range are also taught. After completing several function operations practice problems, your student could be capable of:
- Describing, using and transforming functions
- Adding, multiplying, dividing and subtracting functions
- Using graphs to determine domain and range
- Understanding the process of function composition
- Writing inverse functions and solving sample problems involving the composition of functions
- Identifying and contrasting linear and non-linear functions
Designed with convenience in mind, this chapter's video lessons are self paced, flexible and easy to understand. Your student can enhance what is known about the properties of functions before answering similar questions on the TACHS examination. Clicking on the video, quiz or course tabs brings up relevant content. Your child can also make use of the handy pause, stop and play features. Text transcripts accompany the video lessons, and quizzes can be taken more than once. If your student wishes to learn offline, the quiz results can be printed to paper and studied intermittently throughout the day.
TACHS: Properties of Functions Chapter Objectives
Questions on the properties of functions can appear on the mathematics section of the TACHS examination. The test will also evaluate your child's reasoning abilities along with their language and reading skills. Register for the test via the Internet or by telephone. These methods require a credit card payment for the registration fee. Registration by mail is also possible, and you should mail a cashier's check or money order to cover the fee.
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. 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!
3. 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!
4. 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.
5. 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.
6. 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.
7. 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!
8. Linear and Nonlinear Functions
After watching this video lesson, you'll be able to tell the differences between linear and nonlinear functions. You'll also be able to identify both types just by looking at graphs.
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Other chapters within the Test for Admission into Catholic High Schools (TACHS): Practice & Study Guide course
- TACHS: Vocabulary Practice
- TACHS: Reading Comprehension
- TACHS: Reading Interpretation & Analysis
- TACHS: Technical & Informational Text
- TACHS: Literary Text
- TACHS: Poetry
- TACHS: Language & Spelling
- TACHS: Sentence Structure & Word Usage
- TACHS: Expressing Ideas in Writing
- TACHS: Number Sense & Operations
- TACHS: Basic Arithmetic Operations
- TACHS: Integers
- TACHS: Irrational & Rational Numbers
- TACHS: Inequality Practice
- TACHS: Estimation in Mathematics
- TACHS: Decimals
- TACHS: Fractions
- TACHS: Percent
- TACHS: Ratios & Proportion
- TACHS: Basic Algebraic Expressions
- TACHS: Algebraic Distribution
- TACHS: Square Roots
- TACHS: Exponents & Exponential Expressions
- TACHS: Scientific Notation
- TACHS: Standard Measurement
- TACHS: Introduction to Geometry
- TACHS: Geometric Measurement
- TACHS: Symmetry, Similarity & Congruence
- TACHS: Properties of Lines
- TACHS: The Coordinate Graph
- TACHS: Transformations in Math
- TACHS: Triangles
- TACHS: Triangle Theorems & Proofs
- TACHS: The Pythagorean Theorem
- TACHS: Graphical Representations of Data
- TACHS: Statistics & Data Analysis
- TACHS: Probability & Permutations
- TACHS: Graphing Functions
- TACHS: Factoring
- TACHS: Simplifying & Solving Rational Expressions
- TACHS: Linear Equations
- TACHS: Systems of Linear Equations
- TACHS: Mathematical Patterns
- TACHS: Mathematical Reasoning
- TACHS: Reasoning Abilities
- TACHS Flashcards