Ch 2: Graphing and Functions in AP Calculus: Tutoring Solution

About This Chapter

The Graphing and Functions chapter of this AP Calculus AB and BC Tutoring Solution is a flexible and affordable path to learning about graphing and functions in AP calculus. These simple and fun video lessons are each about five minutes long and they teach all of the operations involving graphing and functions required in a typical AP calculus course.

How it works:

  • Begin your assignment or other AP calculus work.
  • Identify the graphing and functions concepts that you're stuck on.
  • Find fun videos on the topics you need to understand.
  • Press play, watch and learn!
  • Complete the quizzes to test your understanding.
  • As needed, submit a question to one of our instructors for personalized support.

Who's it for?

This chapter of our AP calculus tutoring solution will benefit any student who is trying to learn about graphing and functions for AP calculus and earn better grades. This resource can help students including those who:

  • Struggle with understanding how to graph basic functions and inverse functions, calculate slopes and tangents, identify asymptotes or any other graphing and functions in AP calculus topic
  • Have limited time for studying
  • Want a cost effective way to supplement their math learning
  • Prefer learning math visually
  • Find themselves failing or close to failing their graphing and functions in AP calculus unit
  • Cope with ADD or ADHD
  • Want to get ahead in AP calculus
  • Don't have access to their math teacher outside of class

Why it works:

  • Engaging Tutors: We make learning about graphing and functions for AP calculus simple and fun.
  • Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
  • Consistent High Quality: Unlike a live calculus tutor, these video lessons are thoroughly reviewed.
  • Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about graphing and functions on the go!
  • Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.

Learning Objectives

  • Define functions.
  • Graph basic functions.
  • Graph functions of functions.
  • Graph inverse functions.
  • Factor polynomial functions.
  • Use exponentials to simplify polynomial functions.
  • Describe the basic properties of logarithms and the natural log.
  • Calculate the slopes and tangents of a graph.
  • Use the point-slope formula to determine the equation of a line.
  • Locate horizontal and vertical asymptotes on graphs.
  • Describe the relationship between inverse and implicit functions.

11 Lessons in Chapter 2: Graphing and Functions in AP Calculus: Tutoring Solution
Test your knowledge with a 30-question chapter practice test
What is a Function: Basics and Key Terms

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.

Graphing Basic Functions

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.

Compounding Functions and Graphing Functions of Functions

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!

Understanding and Graphing the Inverse Function

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.

Polynomial Functions: Properties and Factoring

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.

Polynomial Functions: Exponentials and Simplifying

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.

Exponentials, Logarithms & the Natural Log

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.

Slopes and Tangents on a Graph

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.

Equation of a Line Using Point-Slope Formula

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.

Horizontal and Vertical Asymptotes

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.

Implicit Functions

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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