About This Chapter
Below is a sample breakdown of the Graphing and Functions 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 is a Function: Basics and Key Terms; |
Graphing Basic Functions;
Compounding Functions and Graphing Functions of Functions
| An exploration of the use of domain and range; |
Learning how to work with the Cartesian plane;
Composite functions and the process of solving them
|Tuesday|| Understanding and Graphing the Inverse Function; |
Polynomial Functions: Properties and Factoring
| The five steps of this process; |
The processes of graphing polynomials factoring quadratics
|Wednesday|| Polynomial Functions: Exponentials and Simplifying; |
Exponentials: Logarithms and the Natural Log
| The powers of two; |
The use of carbon dating and the rules for working with the natural log and logarithms
|Thursday|| Slopes and Tangents on a Graph; |
Equation of a Line Using Point-Slope Formula;
Horizontal and Vertical Asymptotes
| Determining the steepness of lines on graphs; |
Examples of point-slope form;
The differences between the two
|Friday||Implicit Functions||The process of learning the equations for ovals and circles|
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. 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.
3. 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!
4. 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.
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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