1.3 Functions and Their Graphs

At the heart of calculus lie two fundamental concepts: function and limit. From them are derived additional concepts such as the derivative and integral. Thus, understanding the concept of function becomes the first priority when studying calculus.
By the end of your studying, you should know:
Onscreen applet instructions: For the top applet at the right, click the screen and hold down the mouse button to show a vertical line. For the bottom applet, type a value of x and then the Enter key. 

ExamplesExamine the graph of the equation x^{2} + y^{2} = 4 for symmetry.
Find the domain of the function
Discuss the symmetries (if any) of the function
AppletsSymmetry: Odd and Even FunctionsFunction Grapher
VideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 1.3 Functions and Their Graphs (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"
Information on Leibniz
Calculus Applications
Mathematical Functions

Interesting ApplicationDo you see any functions?

1.2 Lines in the Plane  Table of Contents  1.4 Defining New Functions from Old 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel