# M1110 TB 2.3 Functions

and in a series of ordered pairs a function is such that the X element is only used once in the series of relations so let’s take a look at this an example one it’s to decide whether these are a function or not well let’s take a look at them so here we have a one we have a negative two and a negative three are the X elements repeated know so yes this is a function here we have a 1 111 repeated so this is not a function a negative 4 negative to a negative to the negative 2 is repeated it’s not a function now sometimes you see it shone like this where these are your X values these are your y-values now notice from the X values there’s only one line going from each value so this indicates that these items are only used once so this is a function now in this case we see from the negative 2 which is the x value two lines so that indicates that’s used twice so this is not a function now we’ll also see it in drafts from time to time as you look at that and you graph it notice the X is only used once so this is a graph of a function now a little later we’re going to show you what is called the vertical line test in fact i’ll show it to you right now now in the vertical line test we take a vertical line it’s an imaginary line that we move over the face of the graph now as we do this does this vertical line intersect our graph which are dots here in more than one place so as it goes over this one only one place it goes over this one only one place goes over this one only one place so yes this is a function now here again they’re relating a slope intercept formula to a function where your dependent variable results from putting some value for the X here as you put in some value for an X let’s say a 4 is what they’re showing then 2 times 4 is 8 and 8 is the output so we have this as the input with X the independent variable and then your Y comes out of the system now to tie this in to to graphing let’s say if we have a graph and we make a graph of this where our y-intercept is 0 we put a dot at 0 the slope is 2 over 1 so we go over 1 up to and then we make a line through that and in a sense this is the graph of this function we can change the wide f of X now does this line pass the vertical line test well as we move this line over the face of our graph does it intersect it at only one place as it moves across and the answer is yes so this is a function and that’s what they’re saying here as we go on they’re introducing domain and range which we’ve defined already the domain is the X element the range is the Y element so if you are asked to find the domain and range of a relation here are your coordinates I