1.3 Functions and Their Graphs

 

Summary

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:

  • The definition of a function (rule, domain, range)
  • How to find domains and ranges.
  • How to graph a function.
  • The graphs of some standard functions (e.g., x2, √x, 1/x, |x|).
  • How to classify functions as even, odd, or neither.
  • How to describe even and odd functions in terms of their symmetry.

On-screen 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.

Examples

Examine the graph of the equation x2 + y2 = 4 for symmetry.

Find the domain of the function

Discuss the symmetries (if any) of the function

Applets

Symmetry: Odd and Even Functions
Function Grapher

Videos

See short videos of worked problems for this section.

Quiz

Take a quiz.

Exercises

See 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 Web

Information on Newton
Biographical 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
Biographical data from St. Andrew's University's Web site
Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics"

Calculus Applications
Project Intermath

Mathematical Functions
Wolfram Research

Interesting Application

Do 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