About This Chapter
Graphing and Evaluating Equations and Functions - Chapter Summary and Learning Objectives
This chapter delineates the procedures for graphing various types of functions and equations. These lessons define such concepts as range and domain, introduce formulas for calculating points and distances, and show you how to graph different slopes and inequalities. Tutorials in this chapter are intended to help you:
- Become familiar with the point-slope formula
- Know how to graph basic functions and inequalities
- Understand the distance and midpoint formulas
- Work with functions
|Equation of a Line Using Point-Slope Formula||Use the point-slope formula to solve equations.|
|Graphing Undefined Slope, Zero Slope, and More||Learn how to graph exceptional line types, such as undefined and zero slope.|
|How to Graph 1- and 2-Variable Inequalities||Explore how to express inequalities on a graph.|
|Graphing Inequalities: Practice Problems||Complete practice problems involving 1- and 2-variable inequalities.|
|How to Use the Distance Formula||Recognize how to use the distance formula to calculate the distance between two points.|
|How to Use the Midpoint Formula||Identify the purpose of and understand how to utilize the midpoint formula.|
|Graphing Basic Functions||Know how to graph a function on a Cartesian plane.|
|Compounding Functions and Graphing Functions of Functions||Understand and work with composite functions.|
|Discontinuities in Functions and Graphs||Understand and distinguish among three kinds of function discontinuities.|
|What Is Domain and Range in a Function?||Learn how to determine the range and domain of functions.|
1. 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.
2. Graphing Undefined Slope, Zero Slope and More
There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!
3. How to Graph 1- and 2-Variable Inequalities
So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!
4. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
5. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
6. How to Use The Midpoint Formula
The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.
7. 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.
8. 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!
9. Discontinuities in Functions and Graphs
In this lesson, we talk about the types of discontinuities that you commonly see in functions. In particular, learn how to identify point, jump and asymptotic discontinuities.
10. 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.
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