About This Chapter
Who's it for?
This unit of our High School Precalculus Homeschool course will benefit any student who is trying to learn about graphing functions. There is no faster or easier way to learn about precalculus. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn to graph functions of functions and explain inverse functions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a precalculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a How to Graph Functions unit exam confirm understanding or identify any topics that require review.
How to Graph Functions Unit Objectives:
- Learn to do simple factoring using properties of quadratic functions.
- Calculate and define slopes and tangents on a graph.
- Discover how to determine an equation for a line.
- Discuss the properties of exponentials.
- Learn to identify vertical and horizontal asymptotes.
1. Graphing Basic Functions
Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.
2. Polynomial Functions: Properties and Factoring
Everything from projectile motion to trigonometric functions can be described by polynomials. Review factoring, polynomials and quadratic functions in this lesson.
3. Polynomial Functions: Exponentials and Simplifying
How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.
4. Slopes and Tangents on a Graph
Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.
5. Horizontal and Vertical Asymptotes
No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.
6. Implicit Functions
Sometimes inputting a variable into a function 'black box' doesn't yield a simple output. Find out what happens when you can't isolate the dependent variable on one side of the equal sign.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing Linear Equations: Homeschool Curriculum
- Solving & Graphing Inequalities: Homeschool Curriculum
- Absolute Value Expressions: Homeschool Curriculum
- Graphing Complex Numbers: Homeschool Curriculum
- Solving Linear Systems: Homeschool Curriculum
- Linear Models: Homeschool Curriculum
- Quadratics: Homeschool Curriculum
- Quadratic Functions & Equations: Homeschool Curriculum
- Geometry Basics: Homeschool Curriculum
- Functions for Precalculus: Homeschool Curriculum
- Using Function Operations: Homeschool Curriculum
- Recognizing Graph Symmetry: Homeschool Curriculum
- Rate of Change: Homeschool Curriculum
- Polynomial Functions: Homeschool Curriculum
- Higher-Degree Polynomials: Homeschool Curriculum
- Difference Quotients in Precalculus: Homeschool Curriculum
- Working with Rational Expressions: Homeschool Curriculum
- Evaluating Logarithmic Functions: Homeschool Curriculum
- Functions in Trigonometry: Homeschool Curriculum
- Using Trigonometric Graphs: Homeschool Curriculum
- Trigonometric Equations: Homeschool Curriculum
- Basic Trigonometric Identities: Homeschool Curriculum
- Laws of Sine & Cosine: Homeschool Curriculum
- Graphing Piecewise Functions: Homeschool Curriculum
- Vectors & Matrices: Homeschool Curriculum
- Mathematical Sequences: Homeschool Curriculum
- Identifying Conic Sections: Homeschool Curriculum
- Parametric Equations: Homeschool Curriculum
- Continuity: Homeschool Curriculum
- Limits in Precalculus: Homeschool Curriculum
- Groups & Sets in Algebra: Homeschool Curriculum