If you repeat an x-value it has to have the same y-value
A function may not have two y-values assigned to the same x-value, such as (2,5), (2,7).
A function may, however, have two x-values assigned to the same y-value, such as (2,5), (3,5)
Examples of Functions 1. (2,5) (3,6) (4,7) (8,9)
Examples of Functions 2. (2,5) (3,5) (4,7) (9,10)
Non-examples (2,5) (3,6) (4,7) (4,9)
Notice 4 has two different y values 7 and 9
Today we are going to look at “What is a function? “by looking at ordered pairs. Do these ordered pairs create a function? The answer is yes but how do you know? Let’s look at the rules and then we will come back and explain this example a little bit more. What are the rules to decide if you have a function or not? First, each X or input has only one unique Y output. That is hard to think about so I have an analogy to show you. Think about a coke machine. The X values are like the buttons on the front of the machine if you press the coke button you will get a coke out. If you press the diet coke button you will get a diet coke out and if you press a sprite you will get a sprite out. Can you press a coke and get a diet coke out? No that means it is not functioning correctly therefore it is not a function. A coke button cannot produce a different type of output other than a coke. Now let’s go back and look at with ordered pairs. We have an X value of 1 and we get out a 2 so that is a unique output We push the 2 we get a 5, push the 3 get a 10, we push an 8 get out a 2 that’s OK because we can have different coke buttons getting the same output. We have a 6 getting out a 5 Notice I have two different buttons producing a 6 but what we can’t have is a function as it stands what happens if I say we are going to have the two button and we will get a 10? Now notice I have 2 number 2s (Two different buttons that are coke buttons) First time I get out a 5 the second time I get a 10 that’s not possible I can’t push the same button and two get different drinks. That’s not a function. You look for repeating X values. If you repeat an X value you have to repeat the same Y value. That’s how you decide if you have a function or not given ordered pairs. Thanks for watching
What is a function?
Remember with ordered pairs the x is writen first (x,y)