Today I will talk about relations , relations are a set of inputs and outputs usually Written as an ordered pair and for example (X,Y) there are 3 major ways that you can sort of show relations visually those ways our first you can show is arrow diagram like in the image
Show numbers inside of the first circle and the second circle maybe squares or rectangles or whatever you want, but this relation then is 5 to 7, 3 To negative 2, negative 4 to 4 and 8 to 9 that would be the relation here shown by the arrow diagram
The second way would be in a table where you would list all the X values probably usually x-values are on the left y values on the right
and so this would be 2 to 4, negative 2 to 5 and 4 to negative 6 that would be this table of values here
And the third way that you can often see relations are in the graph
Where you'll have a points and you would give your x value first in this case would be like point 7 or something and then your Y value which would be like two-and-a-half ok so the first point would be . Point 7 and 2.7 and the other point almost 2 and a little over three so those would be the relations will practice a little bit for each of these but that's the basic big idea with relations.
Within a relation there are two parts like I said the X and the Y the X is called the domain and the Y is called the range, so let's identify the domain and the range for these three relations that we have in the image
Our first relation we have the domains of the X values are 5, 3, negative 4 and 8 so we can write our answer, our answer will look a lot like a set ok {5, 3, -4, 8}
so can look like that
And then our range would be the Y values or in this Case 4, 7, 9 and negative 2
Usually what you will do when we're writing the domain and range is just want to point this out is that we will write them in chronological order so we wouldn't right 5, 3, negative 4, 8 instead we would write it actually as negative 4, 3, 5, 8
Alright, we just take the same numbers, but just arrange them in chronological order that be the proper way to actually lift our domain we're going to do the same thing with our range we're going to put it in the proper order so it will be negative 2, 4, 7 and 9
That's just the generally accepted proper format of putting items in a list like this alright
So let's go ahead and look at our domain and range of the table
What's the domain with the x-values I'll list them here and i'm going to go ahead and start by listing them in their chronological order negative 2, 2 and 4 is that what you got for your right domain that should be what you have
And for your range what would you have, if You have negative 6, 4 and 5
as your range In your Y values, then that's correct, that's your domain and your range.
And about our graph
in our graph I've gone ahead on this one actually made them line up so they're going to be nice even numbers on whole numbers ok so our domain or our X values for this graph would be 1, 2 and 3
We go along our x-axis we see that the first one is that 1 the second one is it 2 and the third one is 3
Our range will then go on our Y-axis and again start at the bottom so first one it would be 1 the next one will be 3 and the final one is 4 all right
So that's the way that we would identify our domain or the range inside of relations.
Let's look at one more set of practice questions here identifying the domain and range
And this is the first time i've shown this, this is how you would list a relation this is the way that we would show the full relation so the relation of negative 1, 2; 0, 5; 3, 8 and 5, 9 alright so that is how you would list an entire relation of several sets of ordered pairs together in the X, Y format.
So if we're going to identify the domain of this then what we would do is list again in chronological order all of the X-values so negative 1, 0, 3 and 5
and those values will show you exactly where they came from took the X values in these ordered Pairs negative 1, 0, 3 and 5
that is the domain of these ordered pairs
The next question asks us to find the range of these ordered pairs so i can go ahead and highlight those 5,3, 1 and negative 1
And because we're writing them in chronological order the way we would write this is actually the opposite of what is listed there we'd say negative 1, 1, 3 and 5
That's a good introduction to relations. Have a nice day!
