# MCR-3U Functions

What is a function? Well it's a very common word we use in math, but some don't know the actual meaning of a function. It can be very difficult to understand what a function is. However a simple explaining is taking an input in and creating an output. There is more to that, we can take a persons temperature with a thermometer, which is our input, and creates an output of what the persons temperature is. We use this information to see if the person has a fever or not. Another example might be f(x) = x + 1, our input is this equation and our output could be f(x) = 4 i subbed in 3 for one and created an output of 4. Well how do we know if an equation is not a function? because not everything can become a function, there are 2 ways, one i, when we graph the equation we have to see if any two lines cross each other vertically. This is called the vertical line test,

As we can see here, there are two examples of a vertical line test one being a function and the other not a function. the one on the right has three vertical points that cross on the graph more than once. The other way is to see all the y values and to see if any one of them have the same x value, so here is an example {0,0} {1, 2} {1, 3} We can see that 3 and 2 have the same x value and they will cross the vertical line test, so that means this is not a function. Why is this important? Well lets go back to taking the temperature lets say that a person with a fever is taken a temperature and person who doesn't have one as well they both have the same temperature. Well that obviously doesn't make sense the person with the fever should have a higher temperature, our y value which is their temperature on the thermometer is reading that their temperature is the same but that doesn't make sense. If we don't have functions in our life a lot of day to day basic things we use in our life won't have even existed.