# Ch 1: Graphing and Functions: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering college calculus material will benefit from taking this course. There is no faster or easier way to learn college calculus. Among those who would benefit are:

- Students who have fallen behind in understanding graphing or working with functions
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about graphing and functions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Graphing and Functions chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Graphing and Functions chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any graphing and functions question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

In this chapter, you'll learn the answers to questions including:

- How do I graph functions of functions and the inverse function?
- What steps do I follow when factoring and simplifying in polynomials functions?
- How do I define and calculate slopes and tangents on graphs?
- What do I do to find horizontal and vertical asymptotes?

### 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.

### 12. Normal Line: Definition & Equation

In calculus, a normal line is a line that goes through a point on a curve and is perpendicular with the tangent line at that point. In this lesson, you'll learn more about normal lines and how to find their equations.

### 13. Point of Intersection: Definition & Formula

In this lesson, we'll learn what the point of intersection is and how to find it graphically and algebraically. This concept applies to lots of other areas of study, including business, finance, construction and physics.

### 14. Point Slope Form: Definition, Equation & Example

In this lesson, you will learn the definition and formula for writing the equation of a line in point-slope form. Then, we will look at a couple of examples. At the end, you will be able to test your knowledge with a quiz.

### 15. Point Symmetry: Definition & Examples

Symmetry is a common occurrence and concept of nature and life. In this lesson, we will look particularly at the characteristics of objects that have point symmetry.

### 16. Polar Coordinates: Definition, Equation & Examples

Discover a new way of graphing with polar coordinates. In this lesson, you will learn the definition of polar coordinates, how they can be calculated, and in what types of problems they will be useful. Practice what you have learned with example problems and a quiz after the lesson.

### 17. Negative Reciprocal: Definition & Examples

The negative reciprocal of a number is a very fancy word for a very simple concept. In this lesson, through definition and example, we'll learn how to find a number's negative reciprocal.

### 18. Solving 5 to the 4th Power

What are exponents and how do they work? This lesson explains this process using the example of raising 5 to the 4th power. We'll go over the process step by step.

### 19. Solving 5 to the Negative 4th Power

In this lesson, you will learn the steps of solving 5 to the negative 4th power. In doing so, you will learn the basics of exponents and negative exponents and how to solve them.

### 20. Elliptic vs. Hyperbolic Paraboloids: Definitions & Equations

Paraboloids are three-dimensional objects that are used in many science, engineering and architectural applications. In this lesson, we explore the elliptic paraboloid and the hyperbolic paraboloid.

### 21. Hyperboloids of One Sheet

It is fun to visualize the slices of a three-dimensional math object. In this lesson we use the idea of slices to understand hyperboloids of one sheet.

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### Other Chapters

Other chapters within the Calculus: Help and Review course

- Continuity in Calculus: Help and Review
- Geometry and Trigonometry in Calculus: Help and Review
- Using Scientific Calculators in Calculus: Help and Review
- Limits in Calculus: Help and Review
- Rate of Change in Calculus: Help and Review
- Calculating Derivatives and Derivative Rules: Help and Review
- Graphing Derivatives and L'Hopital's Rule: Help and Review
- Applications of Derivatives: Help and Review
- Area Under the Curve and Integrals: Help and Review
- Integration and Integration Techniques: Help and Review
- Integration Applications: Help and Review
- Differential Equations: Help and Review