About This Chapter
Graphing & Working with Trigonometric Functions - Chapter Summary and Learning Objectives
In this collection of lessons, you can take a look at the foundations of functions, including how and when to use function notation. Learn all about domain, range, power functions, discontinuities and transformations. When you've completed all of the lessons in this chapter, you should have a clear understanding of the topics below:
- Equations of power and radical functions
- Range and domain in functions
- Discontinuities and piecewise functions in graphs
- Shifting graphs on a plane through transformations
|What is a Function: Basics and Key Terms||Learn about function notation and its usefulness.|
|Functions: Identification, Notation & Practice||Review functions and their notations while completing practice exercises.|
|What Is Domain and Range in a Function?||Find out what values aren't allowed in functions, such as negative roots and zero denominators.|
|What is a Power Function? - Definition, Equations, Graphs & Examples||Examine how to write and graph power functions.|
|What is a Radical Function? - Definition, Equations & Graphs||Explore graphs of cube root and square root functions.|
|Discontinuities in Functions and Graphs||Learn all about the concept of discontinuities in both graphs and functions.|
|How to Graph Piecewise Functions||Find out what piecewise functions are and how to graph them.|
|How to Find the Domain of Piecewise Functions||Identify methods for discovering the domain of piecewise functions.|
|Transformations: How to Shift Graphs on a Plane||Demonstrate strategies for shifting graphs on a plane through transformations.|
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. Discontinuities in Functions and Graphs
In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.
7. How to Graph Piecewise Functions
Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.
8. How to Find the Domain of Piecewise Functions
The domain of any function is all the values that x can be for that function. Piecewise functions are special functions that have different parts with unique rules for each part. This lesson will show you how to find the domain for piecewise functions.
9. 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 Algebra 2 and Trig Textbook course
- Identifying Real Numbers
- Complex Numbers
- Absolute Value Review
- Solving Algebraic Expressions & Equations
- Calculating Rational Expressions
- Working with Linear Equations
- Solving & Graphing Inequalities
- Graph Symmetry
- Graphing with Functions
- Solving Linear Equations
- Calculating & Graphing Polynomials
- Calculating & Simplifying Exponential Expressions
- Square Roots & Radical Expressions
- Quadratic Equations & Formulas
- Factoring & Graphing Quadratic Equations
- Conic Sections: Ellipses, Circles, Hyperbolas & Parabolas
- Vectors, Matrices and Determinants
- Exponential Functions & Logarithmic Functions
- Arithmetic & Geometric Sequences & Series
- Calculating & Presenting Statistics
- Combinatorics & Probability
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Equations
- Trigonometric Identities
- Circles, Angles & Circular Arcs