# Ch 3: Graphing and Evaluating Equations and Functions

### 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

Video | Objective |
---|---|

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

The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. Identify the use of point-slope formula in graphing a line through provided examples.

### 2. Graphing Undefined Slope, Zero Slope and More

When the variable determining the slope is mathematically impossible but can still be graphed, it is referred to as an undefined slope. Learn how to compute formulas to graphs that have either undefined slope or zero slopes, and discover what this means for the line.

### 3. How to Graph 1- and 2-Variable Inequalities

The number of variable inequalities in an equation affects how it is solved and graphed. Learn more about the properties of one-variable and two-variable inequalities and how to graph them on number lines and coordinate planes.

### 4. Graphing Inequalities: Practice Problems

Whether an inequality has one or two variables is an important distinction when graphing these types of algebraic expressions. Learn more about when to use a number line or a coordinate plane when graphing inequalities by solving some practice problems.

### 5. How to Use The Distance Formula

The distance formula is a shortened form of the Pythagorean Theorem. Learn about the Pythagorean Theorem and the distance formula, along with examples of how the formula is used.

### 6. How to Use The Midpoint Formula

The midpoint formula enables us to find the midpoint of a line segment when we know the endpoints. Learn about line segments, midpoints, and how to use the midpoint formula. Explore examples, and understand that the midpoint can be found on both vertical and horizontal line segments.

### 7. Graphing Basic Functions

Graphing basic functions on a Cartesian plane is similar to finding a spot on a map. Learn more about the similarities between maps and graphs, the functions of ordered pairs and quadrants, and how to graph their functions.

### 8. Compounding Functions and Graphing Functions of Functions

In mathematics, functions are used to explore the relationships between numbers, using inputs and operations to produce outputs. Learn about compounding functions and the process of graphing the functions of functions, and further your understanding by reviewing composite functions, including their domain and range.

### 9. Discontinuities in Functions and Graphs

A discontinuity is where the potential values in an equation 'jump', rather than being continuous as with an un-broken line on a graph. See how discontinuities appear in graphs and equations, including jump discontinuities and asymptotic discontinuities.

### 10. What Is Domain and Range in a Function?

The domain is the set of all the allowable input values of a function, while the range is the set of all possible output of the function. Learn how to find the domain and range of a function through given values, graphs, or general function rules.

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