About This Chapter
Below is a sample breakdown of the Functions: Precalculus chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||What are functions used for?||The symbol f, x variable, y variable, y = f(x), function identification, function notation, and the vertical line test|
|Tuesday||Range and domain||Possible inputs, possible outputs, graph squishing, real numbers, dividing by zero, and general rules for range|
|Wednesday||Power functions||Understanding the formula f(x) = kx^n, graphs of power functions, parabolas, and symmetry|
|Thursday||Radical functions||Understanding the importance of domain prior to graphing radical functions, quadratics, u-shaped graphs, and inequality equations to avoid complex numbers|
|Friday||Transformations||Translation, rotations, reflections, dilation, how adding or subtracting affects how the graph shifts, and f(x - h) + k|
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 Syllabus Resource & Lesson Plans course
- Linear Equations: Precalculus Lesson Plans
- Inequalities: Precalculus Lesson Plans
- Absolute Value Equations: Precalculus Lesson Plans
- Complex Numbers: Precalculus Lesson Plans
- Systems of Linear Equations: Precalculus Lesson Plans
- Mathematical Modeling: Precalculus Lesson Plans
- Solving Quadratics: Precalculus Lesson Plans
- Quadratic Functions: Precalculus Lesson Plans
- Geometry Basics for Precalculus Lesson Plans
- Function Operations: Precalculus Lesson Plans
- Graph Symmetry: Precalculus Lesson Plans
- Graphing with Functions: Precalculus Lesson Plans
- Rate of Change: Precalculus Lesson Plans
- Polynomial Functions: Precalculus Lesson Plans
- Advanced Polynomial Functions: Precalculus Lesson Plans
- Rational Functions & Difference Quotients: Lesson Plans
- Rational Expressions & Function Graphs: Lesson Plans
- Exponential & Logarithmic Functions: Lesson Plans
- Trigonometric Functions: Precalculus Lesson Plans
- Trigonometric Graphs: Precalculus Lesson Plans
- Solving Trigonometric Equations: Lesson Plans
- Trigonometric Identities: Precalculus Lesson Plans
- Trigonometric Applications: Precalculus Lesson Plans
- Graphing Piecewise Functions: Precalculus Lesson Plans
- Vectors, Matrices & Determinants: Lesson Plans
- Mathematical Sequences & Series: Lesson Plans
- Sets in Algebra: Precalculus Lesson Plans
- Analytic Geometry & Conic Sections: Lesson Plans
- Polar Coordinates & Parameterizations: Lesson Plans
- Continuity: Precalculus Lesson Plans
- Limits: Precalculus Lesson Plans