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Week 11 – Math 11 – Domain and Range

Domain and range refers to how much on number on either the x or y axis can vary by, visually, it is a section on a graph that shows the lowest and highest possible x and y value where domain is used for the x axis and range is used for the y axis.

The first step of finding domain is looking for the furthest two points on the x axis that the line goes, in this example we see that the lowest x value used or the point furthest to the left is 1 and our highest x value is 6.

After finding out your lowest and highest x value, writing the domain in an expression has two different variations, set notation and interval notation, the difference between the two is that set notation is a bit clearer and usable with graphs using discrete variables while interval notation can be a bit more vague but saves time to write.

Writing set notation for the domain of this line goes: D = {1 ≤ x ≤ 6}, start with writing that this expression is about a domain, write the lowest number first, add the appropriate sign in relation to x, (≤ is used when the point you are referring to has a closed dot while < is used when that point has an open dot instead) put the variable that is in between both numbers, add the appropriate ≤ or < sign again, then put the highest value of x and put everything in curly brackets if your line goes on forever in one direction you only write the relation of the given number and x but if it goes on forever in both ways it means that x can be any possible real number which can be written as D = xER meaning x is an element of real numbers.

Set notation is a lot more simple as it looks like D = [1, 6] for this line, all you do is list both numbers and use appropriate brackets instead of ≤ or < where [] is used with closed dots and () is used with open dots and infinity, both notations mean the same thing so it comes down to preference or if a graph uses discrete variables or not.

Finding the range of a line works the exact same as domain but with the y axis, find the highest and lowest y values which are 3 and 6 in this case and make sure to use appropriate signs and brackets depending on open or closed dots, with this line set notation would look like R = {3 ≤ y ≤ 6} and interval notation would look like R = [3, 6]

 

Published inMath 10

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