Week 12 of Math 10, and Week 2 of online classes. We’ve gone further into relations through domain and range then moved on to functions. However, domain and range was one of the more difficult topics that I have dealt through, so despite my doubts, I’m going to take it upon myself to try and explain it to make sure I remember what I learned. In this blog post I will be detailing what domain and range is and how to interpret it into set notation.

So, first let’s explain what they are. Domain is the set of all possible numbers on the x-axis, while Range is the set of all possible numbers on the y-axis. You can find the domain and range through a variety of ways such as ordered pairs and graphs, like this one:

Here you can see two pairs of open dots, two on the x-axis and two on the y-axis. To make things easier we will deal with the domain first. Start off by looking for the smallest value that has a dot, which in this case is -4, then look for the biggest value that has a dot which is 6. We format domain and range through set notation which looks like this:

Set notation starts off with the smallest value on the left most side, followed by a less than sign and a variable (usually is x but can vary from question to question) and that variable is also followed by another less than sign and the biggest value. Usually questions that have two points follow this format.

To make things easier, think of x as the stretch between -4 and 6, x has to be bigger than -4, but can only be smaller than 6.

There can also be graphs that have lines with arrows in them, like this one.

These ones are a bit more complicated, as the arrow indicate that the line will continue to go on infinitely. Luckily there is a way to express that in set notation as well. For the domain the smallest value is 2, but since the x is in front of 2 and there’s a shaded dot, x has to be greater than or equal to 2.

Normally {} would be the final result, but because there’s an arrow, x can go on forever and it would be unreasonable to attempt to label every single possible number, we will instead use x∈R or x is an element of real numbers, so the domain would be {, x∈R } For the range, there aren’t any two points we can calculate, so the range is simply 0.

Finally, there’s a graph that has two arrows

This graph will be using rules from the previous questions. Here -5 is the smallest value on the x-axis, and since there are arrows infinitely going to the right, the answer will be {, x∈R}. For the range however, the lines with arrows have a slight curve to them, meaning they will infinitely go up for the upper line and down for the lower line. So it would mean that all numbers along the y-axis are possible numbers. So in order to simplify things, y∈R or y is an element of real numbers will be used for the range because there is no set point for the y-axis.

And that’s how Domain and Range works

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