About This Chapter
HSPT Test: Properties of Functions - Chapter Summary
The lessons and assessments inthis chapter have been assembled to help students, like you, improve their understanding of functions and mathematical operations with functions. Follow along with our expert instructors in these videos to prepare for questions on the HSPT that may require you to know:
- Basic properties of functions
- How to transform graphs on a plane
- Processes of adding, subtracting, multiplying and dividing functions
- Domain and range of a function
- Steps in composing functions
- Inverse, linear and nonlinear functions
Following each lesson, take the corresponding quiz to identify the topics you don't understand. Then, to improve your understanding of the material, use the video tags from the quiz results to return to and study the parts of the lesson that explained these topics. After you finish the lessons and quizzes of this chapter, assess your comprehensive knowledge of the material presented in them by taking the chapter exam.
HSPT Test: Properties of Functions Chapter Objectives
The purpose of the HSPT is to measure the academic skills of 8th-grade students entering high school. Select Catholic high schools use the results from this exam to help them make admission, scholarship, and placement decisions. When you take this exam you will be asked to complete a series of 298 multiple-choice questions, all in a two-hour and 30-minute testing session. Around 64 of these questions are part of the mathematics section. Use this chapter to prepare for any questions in the mathematics section that may ask you about functions.
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 HSPT Test: Practice & Study Guide course
- HSPT Test: Quantitative Reasoning
- HSPT Test: Mathematical Sequences & Series
- HSPT Test: Understanding Real Numbers
- HSPT Test: Operations in Math
- HSPT Test: Understanding Integers
- HSPT Test: Irrational & Rational Numbers
- HSPT Test: Solving & Graphing Inequalities
- HSPT Test: Using Estimation in Mathematics
- HSPT Test: Using Decimals
- HSPT Test: Understanding Fractions
- HSPT Test: Using Percents
- HSPT Test: Ratios & Proportion
- HSPT Test: Square Roots
- HSPT Test: Exponents & Exponential Expressions
- HSPT Test: Scientific Notation
- HSPT Test: Standard Measurement
- HSPT Test: Introduction to Geometry
- HSPT Test: Perimeter, Area & Volume
- HSPT Test: Symmetry, Similarity & Congruence
- HSPT Test: Properties of Lines
- HSPT Test: Plotting Graphs
- HSPT Test: Transformations
- HSPT Test: Triangle Basics
- HSPT Test: Triangle Theorems & Proofs
- HSPT Test: The Pythagorean Theorem
- HSPT Test: Graphing Data
- HSPT Test: Data Analysis
- HSPT Test: Probability & Permutations
- HSPT Test: Graphing Functions
- HSPT Test: Factoring in Algebra
- HSPT Test: Basic Algebraic Expressions
- HSPT Test: Algebraic Distribution
- HSPT Test: Solving Rational Expressions
- HSPT Test: Linear Equations
- HSPT Test: Systems of Linear Equations
- HSPT Test: Mathematical Reasoning
- HSPT Test: Verbal Reasoning
- HSPT Test: Basics of Grammar
- HSPT Test: Spelling & Punctuation
- HSPT Test: Syntax & Sentence Structure
- HSPT Test: Interpreting Readings
- HSPT Test: Reading Comprehension
- HSPT Test: Understanding Meaning in Reading
- HSPT Test Flashcards