 In this video we present the solution to question number 11 for practice exam number one of math 1210 you are asked to graph the function f of x equals negative 2 times the square root of x minus 2 plus 3 and we need to graph that in the grid lines provided over here and it is going to ask you to label indicate three points on the graph this is mostly so that I can read your graph more accurately when it comes time to grade it and we're supposed to also indicate which transformations were applied from the original function y equals the absolute value of x so that's our basic function right here which remember the absolute value of the absolute value of x I'm going to use the line right here it'll look like that v shape it goes through 0 0 1 1 2 2 3 3 so that's the basic grade that's that's the absolute value function we need to indicate which transformations have been applied to it then so what are some things to see because there's a negative sign in front of the absolute value we're going to see that in terms of transformations there's going to be reflection reflection across the x axis this factor of two corresponds to a vertical stretch so there's going to be a vertical a vertical stretch by two that's the second transformation the third transformation comes about from this negative two inside of the the absolute value this would be in the horizontal zone so this is actually going to be a shift right by two and then lastly this plus three right here this indicates that you're going to have a shift up by three so you're going to want to make sure you list all four of these transformations so let's see then what happens to the graph when it comes to absolute value I want to start with the vertex and see what happens to it the vertex is unaffected by reflections and vertical stretches or compressions um horizontal stretches compressions as well the only thing will affect the vertex will be the shifting so we're going to shift two to the right and three up and so then the vertex is going to be at the point two comma three I would label that on the graph so another point to pay attention to is what happens to the original point one comma one well when you reflect it across the x axis that's going to go to the point one negative one and then when you stretch it that'll go to one negative two then we have to do some shifting we're going to shift two to the right and then three ups of one two three so the final location is going to be right here I'm going to erase my other pictures and put this point right here this is the point three comma one connecting the dots because this is an absolute value function that would give us half of the graph for which we can do this again with the point one comma negative one which was on the original graph but the fact that a absolute value function is symmetric with respect to its vertex I'm just going to use your reflection to find there's another point over here which we're going to graph that right here this would be the point one comma one and then connecting the dots we see this would be the graph of our absolute value function