About This Chapter
Overview of Functions - Chapter Summary
A function is really just a rule that takes a number and transforms it into another number. In this chapter, you can learn the basics of working with functions and complete ample practice problems in applying function operations. The following topics are included in the lessons:
- Foundations of functions
- Graph shifts on a plane for transformations
- Addition, subtraction, multiplication and division of functions
- Range and domain in functions
- Composition of functions and inverse functions
You can watch the short video lessons and then refer to the text transcripts as needed. After you complete a lesson, you can take the quick quiz to measure your learning. If you need to review any topics, the handy video tags can quickly guide you to just the right section in the videos. Some lessons even include links to additional text-only lessons on related topics for additional support.
Integrated Algebra Regents Exam Objectives
The Integrated Algebra Exam transitions into the Algebra I test, as New York completes its changeover to the Common Core Learning Standards. All high school students must pass five subject-area tests with scores of 65 or higher in order to graduate.
In this algebra test, the portion that assesses your understanding of function concepts constitutes about 32%-38% of the three-hour exam. Multiple-choice questions are included, for which our online quizzes can provide valuable practice.
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!
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Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course
- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards