# Ch 11: Graphing with Functions

### About This Chapter

## Graphing with Functions - Chapter Summary and Learning Objectives

Take advantage of the video lessons in this chapter to learn graphing basics for polynomial functions. Our instructors introduce you to some real-world applications for the slopes, tangents and asymptotes depicted in the graphs of quadratic functions, trigonometric functions and more. You can also get an introduction to the basic properties of exponents and the methods used to simplify or factor polynomial expressions. By the time you reach the end of this chapter, you should be able to do the following:

- Factor quadratic expressions
- Simplify exponents in polynomial functions
- Find the slope of a line and identify tangents
- Describe implicit functions and asymptotes

Video | Objectives |
---|---|

Graphing Basic Functions | Review components of the coordinate plane, including the x- and y-axes, origin and quadrants. |

Polynomials Functions: Properties and Factoring | Learn what a polynomial is and explore methods for factoring quadratic functions. |

Polynomials Functions: Exponentials and Simplifying | Explain the addition, multiplication, division and powers properties of exponents. Use them to simplify polynomial functions. |

Slopes and Tangents on a Graph | Explore methods for calculating slopes and tangents on a graph. |

Horizontal and Vertical Asymptotes | Learn to identify horizontal and vertical asymptotes. |

Implicit Functions | Explain the connection between inverse and 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. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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

Other chapters within the Precalculus: High School course

- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations
- Continuity
- Limits