About This Chapter
Functions: Basics for Precalculus - Chapter Summary and Learning Objectives
This functions chapter begins by covering the basics - like function notation and graphical representations of domain and range - so that by the time you reach the remaining lessons, you'll be prepared to study methods for altering the shape and position of a function's graph. You can also explore the applications of functions that include square or cube roots to get ready for topics covered in the precalculus lessons to come. Use the video lessons and quizzes included here, and learn how to do the following:
- Properly use function notation
- Identify a function's domain and range
- Graph radical and power functions
- Transform a function's graph
|What Is a Function: Basics and Key Terms||Explore how functions are used in everyday life. Learn how independent and dependent variables are represented in a function's equation. Examine definitions of domain and range.|
|Functions: Identification, Notation & Practice Problems||Get additional instruction on function notation. Find out how the vertical line test can be used to identify whether the graph of an equation is a function.|
|What Is Domain and Range in a Function?||Learn how to find a function's domain and range by examining input and output values or its graph. Identify values that aren't allowed in a function, such as a negative root or a zero denominator.|
|What Is a Power Function? - Definition, Equations, Graphs & Examples||Find out how to recognize odd, even and fractional power functions and their graphs.|
|What Is a Radical Function? - Definition, Equations & Graphs||Examine methods for graphing square root and cube root functions.|
|Transformations: How to Shift Graphs on a Plane||Understand how to perform rotations, dilations, translations and reflections to graphs on the coordinate plane.|
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. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
3. 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.
4. What is a Power Function? - Definition, Equations, Graphs & Examples
Power functions have many different varieties of graphs. Use this lesson to distinguish the difference between different types of power functions. Test your knowledge with a short quiz after the lesson!
5. What is a Radical Function? - Definition, Equations & Graphs
Radical functions operate very differently than regular functions. This lesson covers the definitions, equations, and graphs that you will need to know to be successful with radical functions.
6. 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!
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Other chapters within the High School Precalculus Textbook course
- Working with Linear Equations
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Polynomial Functions Basics
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Graphing Piecewise Functions
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Sets in Algebra