About This Chapter
Algebra II: Graphing and Functions - Chapter Summary
In mathematics, we often examine the relationships between numbers, including the relationships between the inputs and outputs of equations. These lessons provide a thorough explanation of how to use graphing and functions to note the relationships between numbers and to solve problems. Our lessons have been prepared by experienced educators with extensive knowledge of advanced mathematics. They know the concepts you need to go over, and they can explain each concept in an easy-to follow lesson format. Furthermore, besides providing you with key terms, definitions, and formula examples, our instructors also use real world examples, allowing you to grasp the applications of these topics. By the close of the chapter, you should be prepared to:
- Describe the basic functions of graphing
- Identify the graphing and compounding functions of functions
- Analyze how to graph the inverse function
- Check out factoring and the properties of polynomial functions
- Examine simplifying polynomial functions and exponentials
- Define the natural log, logarithms, and exponentials
- Compare tangents and slopes on a graph
- Explain the point-slope formula to show the equation of a line
- Point out vertical and horizontal asymptotes
- Offer examples of implicit functions
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. 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!
3. 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.
4. 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.
5. 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.
6. 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.
7. Exponentials, Logarithms & the Natural Log
Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.
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. 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.
10. 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.
11. 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 Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II