About This Chapter
Who's It For?
Anyone who needs help learning or mastering AP calculus material will benefit from taking this course. There is no faster or easier way to learn AP calculus. Among those who would benefit are:
- Students who have fallen behind in understanding how to graph 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 in AP calculus
- 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 in AP calculus 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 in AP calculus chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question on graphing and functions. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in a graphing and functions unit of a standard AP Calculus AB and BC course. Topics covered include:
- Graphing basic functions
- Compounding functions
- Graphing functions of functions
- Graphing inverse functions
- Factoring polynomial functions
- Using exponentials to simplify problems
- Calculating slopes and tangents on a graph
- Using point-slope formula to determine the equation of a line
- Identifying horizontal and vertical asymptotes
- Understanding implicit functions
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. Arc Length: Definition & Equation
Arc length is an important aspect to understanding portions of curved lengths. As you will learn in this lesson, combining our knowledge of circumference and central angle measures allows us to find arc length.
13. Arc Measure: Definition & Formula
Arc measure is a way of identifying an arc. In this lesson, we'll learn how to define and calculate arc measure while discussing the different elements involved in this calculation.
14. Finding Instantaneous Rate of Change of a Function: Formula & Examples
In this lesson, you will learn about the instantaneous rate of change of a function, or derivative, and how to find one using the concept of limits from Calculus.
15. Natural Log: Rules & Properties
The natural log (ln) is the logarithm to the base 'e' and has extensive uses in science and finance. This lesson will define the natural log as well as give its rules and properties.
16. Washer Method in Calculus: Formula & Examples
In this lesson, you will learn how the washer method makes your calculus life a little easier by giving you an easy formula and procedure for finding the volume of various shapes created by simple (and not-so-simple) functions.
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Other chapters within the AP Calculus AB & BC: Help and Review course
- Functions in AP Calculus: Help and Review
- Sequences and Series in AP Calculus: Help and Review
- Limits in AP Calculus: Help and Review
- Continuity in AP Calculus: Help and Review
- Exponentials and Logarithms in AP Calculus: Help and Review
- Exponents and Polynomials in AP Calculus: Help and Review
- Applications of Derivatives in AP Calculus: Help and Review
- Calculating Derivatives & Derivative Rules in AP Calculus: Help & Review
- Calculus - Derivatives Calculations & Rules: Help & Review
- Differential Equations in AP Calculus: Help and Review
- Area Under the Curve and Integrals in AP Calculus: Help and Review
- L'Hopital's Rule & Graphing Derivatives: Help & Review
- Integration Applications in AP Calculus: Help and Review
- Rate of Change in AP Calculus: Help and Review
- Geometry and Trigonometry in AP Calculus: Help and Review
- How to Use Scientific Calculators for AP Calculus: Help and Review