the focus of this lesson is on the cubing function f of X equals x cubed now what we're gonna look at is the graph of this function and focus on the different characteristics that it has and the first property that we're going to focus on is the domain so when you think about a graph it's made up of an infinite number of points so some X comma Y's and when we talk about the domain we're focusing on the x coordinates so in other words for this graph which x coordinates are present if you will and so if we were to take this graph and project it onto the x axis where would we hit and we could see that all the way out at negative infinity we are hitting because our graph is continuing forever ever downward and leftward and so all the way out here at negative infinity our graph is hitting the x coordinates and if we keep going along there's no gaps and there's no holes and we now continue to go on in the positive direction forever and ever and ever because of this arrow up here it signifies that it's going up and rightward forever and ever and ever and so we can see from my pink line here that I projected onto the x-axis that if this graph smashed down on the x-axis we would hit at negative infinity to infinity and so we would say that is the interval for the domain and so that is another fancy way of saying all real numbers now let's focus on the range so when we think about the points on the graph instead of focusing on the x-coordinates like we do for domain for range we're gonna focus on the y-coordinates so instead of thinking left to right like we do for domain we're gonna think bottom to top and so if we look at our graph we have this arrow that signifies that it's going forever downward so as far as the range goes we're starting at negative infinity and then there are no gaps like if you take this graph and you project it on to the y-axis smash it onto the y-axis this way and that way you can see that there are no gaps and there are no holes and so we're hitting everywhere and then there's this upward arrow on the actual original graph that signifies that we're going to continue on to positive infinity so again for the range we'd say that it has the interval negative infinity to infinity and so again it's all real numbers