the focus of this lesson is on the square root function f of X equal square root of X which is pictured here graphically and we're going to go ahead and look at the different properties of this function and particularly we're gonna start with the domain and so if you recall a graph has a set of infinite points that are X comma Y and so when we talk about the domain we're talking about the x coordinates of the graph and so if you look at the at the graph that's pictured here you can see that it doesn't have any negative x coordinates in fact it doesn't have an x coordinate until you get to 0 and then as you move along you can see that the positive x coordinates do align with points on the graph and so in other words if you were to take your graph of f of X equals square root of x and project it down onto the x-axis you would see that it starts at x is 0 and then if you continue to project it down you would project it down forever in the positive direction and so it's continuing out to positive infinity and so the interval that we would use to represent that domain would start at 0 and it would include 0 itself and so that's why we use a bracket to say that we're including the 0 and then it goes to positive infinity and you never include positive infinity so you would put a parenthesis and so the domain goes from 0 to infinity which is all the positive real numbers now for the range of the square root function we would think from bottom to top you know again range deals with the y coordinates so what Y coordinates are present on this graph and as you can see if we start here at the bottom and the negative values there is no graph in fact we don't get to graph until we get again to the Y value of 0 so starting here and then as we go upward we continue to hit graph if you think about it if you think about your graph projecting onto the y-axis it continues and continues and continues to hit the higher and higher you go it's because this arrow is indicating that the graph is going out to the right and up forever and ever and so that takes us out to positive infinity and so the interval is represented by the pink line that I'm drawing that starts at zero and continues out to positive infinity so we would say the range again includes the value of zero hence the bracket and goes to positive infinity so again it's all positive real numbers