Skip to main content
Search IntMath

450+ Math Lessons written by Math Professors and Teachers

5 Million+ Students Helped Each Year

1200+ Articles Written by Math Educators and Enthusiasts

Simplifying and Teaching Math for Over 23 Years

Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.

New applet: Domain and range investigation

By Murray Bourne, 09 May 2017

I recently added a new interactive applet that helps you explore the concepts of domain and range. This accompanies one of the most popular pages on IntMath, Domain and Range of a Function.

Most students don't have much trouble with finding the domain of a function (by avoiding negative values under a square root, or zero values in the denominator of a fraction), but figuring out the resulting range can be a challenge.

Many of us are visual learners and it's certainly true that if you have a reasonable idea of what a function looks like in general, then determining the domain and range is a lot easier.

For some examples of what I mean,

  • A linear function (like y = 3x + 2) has no restrictions on the x-values, and all y-values will result
  • A quadratic function (like y = 2x2 − 5) has no restrictions on the x-values (the domain), but only half of the possible y-values (the range) on the plane will be output
  • A sine function (like y = 4 sin x) has no restrictions on the x-values, and all the resulting y-values will be between 4 and −4.
  • A hyperbola (like y = 3/x) is not defined for x = 0, and the resulting y-values will be all values except 0.

How do I know these? It's from having a good idea of what each function looks like in general. I then just need to look at the specific numbers involved and can determine the domain and range without drawing a graph. But how do you learn the general shapes?

The new applet

The new interactive domain and range interactive applet allows you to explore several different functions and see what effect a change in domain makes to the range.

Here are some screen shots:

domain and range - sine curve
Domain and range of a sine curve

This next one has a restriction on the domain:

domain and range - restricted parabola
Domain and range of a parabola with restricted domain

There are also ones with discontinuities:

domain and range - hyperbola
Hyperbola domain and range

Technical bit

To produce the graphs, I'm using AsciiSVG-IM.js, which creates an SVG (scalar vector graphics) image. Here's some background and a demo: AsciiSVG-IM.js Syntax and Demo. I also used this small library for the Online Graphing Calculator and Riemann Sums - Negative Integrals and Discontinuities.

Let me know what you think in the comments below.

Be the first to comment below.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.