About This Chapter
Calculus: Graphing and Functions
In this video lesson series on graphing and functions, you'll learn about the most important pillar of calculus - functions - and understand how to properly graph them. Essentially, functions have an input and an output, which match a set of numbers to another set of numbers. The input (x) and output (y) make up the common function notation, y = f(x). With functions, you'll learn how to determine the domain and range, which are all possible input values and all possible output values, respectively.
Now, it's important to understand the different parts of the graph, which can be thought of as a mathematical map. You'll learn the parts of the Cartesian plane, which include the horizontal x-axis, the vertical y-axis and four quadrants. You'll also learn how to plot points through x and y coordinates, which act like a map's latitude and longitude. Point-slope formula will help you determine the steepness of a graphed line and you'll see how inverse functions create mirror images of functions on a graph.
Your knowledge of functions will then increase through lessons on inverse functions, functions of functions, compounding functions, exponentials and logarithms, slopes and tangents, implicit functions, horizontal and vertical asymptotes, factoring and composite functions.
Sound like a lot? Well, with several mathematical stories and animated graphics included in these videos, the complexities of calculus may be easily understood through these lessons.
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.
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Other chapters within the Math 104: Calculus course
- Vectors in Calculus
- Geometry and Trigonometry
- How to Use a Scientific Calculator
- Rate of Change
- Calculating Derivatives and Derivative Rules
- Graphing Derivatives and L'Hopital's Rule
- Applications of Derivatives
- Area Under the Curve and Integrals
- Integration and Integration Techniques
- Integration Applications
- Differential Equations
- Studying for Math 104