In real world, we always encounter a pair. For example, the kilogram of rice and the money that you need to purchase it. The amount of energy to spend in lifting weights, your feelings towards your crush and more pairs that you will encounter are best representation of ordered pairs. It is somewhat related to something called relation, it is defined as set of ordered pairs.
Ordered pair has two elements called domain and range and can be represented by (x, y) where the set of x is called domain while the set of y as range. Hence, these two variables are interrelated to each other.
Now, we also have something called function. We can determine if the ordered pair is a function if the domain is not repeated in a set. For example, (1,2) (2, 3) (3, 4) (4,5) as what you have noticed, there are 4 x’s in the set and they are 1, 2, 3, and 4 which are different from each other in the whole set. In this case, we can call it as a function. You can also call this set as a relation, remember, all functions are relation but not all relation are function.
To understand it more, we can use a table of values to see the set easier and not complicated.
In this case, you will see that no element of x is repeated, hence, it is called as a function. For the second example, we can use an ordered pair to determine if the set is a function or not.
Example 2:
(1,2) (0,1) (1, 3) (4, 5) (1,6) now, in this example, the set is determined as not a function since there is an element of x repeated which is 1. No matter how the domain is repeated, the set is considered as not a function.
Can we use this in real life situation?
When we are studying mathematics, we always heard “We cannot apply this in real life situation, what is the point of studying this?” Well, actually we can apply this topic in real life situation by using people as an example.
Example 3:
As you can see on the diagram, Gerald like Julia, Bea, Kim, Sarah, and Maja while Ronin likes Sarah only. Gerald and Ronin are the representation of the domain of the set where Julia, Bea, Kim, Sarah, and Maja are the range. Since Gerald is paired to many girls, this set is not a function.
To give you a short way to determine if the ordered pair and table of values are function or not, you can remember this. One-to-one, one-to-many, and many-to-one.
Now that we already know the ways of knowing if the ordered pair and table of values are function or not, we will go to the next which is determining if the graph is a function or not. Honestly, this is easier than what you think, you can easily determine it by just looking on the graph to the point that even pre-school can answer it.
To determine if the graph is a function or not, you need to use a tool called vertical line test, just put a vertical line on the graph and if the line intersect into the graph at only one point, then the graph is considered as a function. Otherwise, if it intersects more than one, the graph is not a function. In this example, the blue graph intersects at only one point using the vertical line test. Hence, the graph is a function.
Overall, this topic is just basic of math. It is easy to determine if the given relation is a function. You can also determine if the equation is a function, but it is almost the same of determining the graph of an equation. It is important to know the basics because it will be your foundation in higher math. Remember that math is everywhere!
Author’s note: Finally, I posted the first blog related about mathematics. If laziness will not hit me, expect more math topics because I will use this opportunity to refresh the topics that we studied, earn, and learn. I am refreshing our school modules and found out that I really need to read them again to recall and I think this is the best way to do it.
They said you will learn when you teach the lessons you studied before, it is a great way to review and recall! I hope that everyone will support this and my upcoming contents, little did you know that math is full of fun and it is everywhere! You can really apply it in real-life situation.
Published: November 27, 2021
Na amazed ako sa sample mo. Hehe. Si Gerald Anderson talaga. Hehe. Lahat ata naging girls niya puro shampoo models.