# 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*= 3*x*+ 2) has no restrictions on the*x*-values, and all*y*-values will result - A
**quadratic function**(like*y*= 2*x*^{2}− 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:

This next one has a restriction on the domain:

There are also ones with discontinuities:

## 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.

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