About This Chapter
Algebra II: Properties of Functions Review - Chapter Summary and Learning Objectives
If you need help sorting out the differences between a function's input and output variables, instructors teaching this chapter have got you covered. Use the video lessons and quizzes included here to review functions' components as well as their notation and graphs. There are even practice problems and multiple-choice quizzes to help you get the processes involved in performing function operations down pat. By the time you reach the end of this chapter, you should be able to do the following:
- Perform arithmetic operations with functions
- Transform a function's graph
- Determine a function's domain and range
- Compose functions
- Find a function's inverse
|What Is a Function: Basics and Key Terms||Learn how to write and use function notation.|
|Transformations: How to Shift Graphs on a Plane||Perform rotations, reflections, dilations and transitions to shift graphs on the coordinate plane.|
|How to Add, Subtract, Multiply and Divide Functions||Examine the steps involved in performing basic arithmetic operations with functions.|
|What Is Domain and Range in a Function?||Outline rules for finding a function's domain and range. Determine which values are acceptable in a function.|
|How to Compose Functions||Explore the processes involved in composing functions.|
|Inverse Functions||Find and confirm the inverse of a function using the horizontal line test.|
|Applying Function Operations Practice Problems||Solve sample problems by composing functions, determining a function's domain and range and finding the inverse.|
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 Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II