About This Chapter
Algebra II: Graphing Polynomial Functions - Chapter Summary
High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on graphing polynomial functions.
Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:
- Outline the properties of polynomial functions
- Explain factoring, exponentials and simplifying with relation to polynomial functions
- Find the equation of a line using the point-slope formula
- Describe implicit functions
- Discuss compounding functions and graph functions of functions
- Understand and graph the inverse function
- Graph y=sqrt(x)
- Define slopes, tangents, and horizontal and vertical asymptotes
1. 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.
2. 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.
3. Equation of a Line Using Point-Slope Formula
It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.
4. 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.
5. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
6. Understanding and Graphing the Inverse Function
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
7. How to Graph y=sqrt(x)
This lesson will show us how to graph the square root function y=sqrt(x). We will look at some of the function's properties, how this graph behaves, and two different ways to go about graphing the function.
8. 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.
9. 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.
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Other chapters within the High School Algebra II: Homeschool Curriculum course
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations Review
- Algebra II: Absolute Value Review
- Algebra II: Inequalities Review
- Algebra II: Working with Real Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Factoring Review
- Algebra II: Quadratic Equations Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Complex and Imaginary Numbers
- Algebra II: Rational Expressions Review
- Algebra II: Polynomials Review
- Algebra II: Polynomials Overview
- Algebra II: Conic Sections
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics Review
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistical Analysis
- Algebra II: Trigonometry Review
- Algebra II: Trigonometry Overview
- Algebra II: Assignments & Projects
- Homeschool Resources for High School Algebra II