Get the free reteaching 27 a preview of transformations - cbennett nuames

NAME CLASS DATE Reteaching 2.7 A Preview of Transformations Skill A Identifying and describing transformations of a function Recall The functions f(x) x 2, f(x) x, and f(x) x are called parent functions.

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HELLO, Mr. Narrow Today we are doing a video introducing transformations. Specifically, we are going to pick apart this parent function of y equals the square root of x. We are going to take this parent function y equals the square root of x and see what this function likes like as it sits right now. Let's make a t-table with this value (equation) and use some values for x like 0, 4, 9, 16. Let's see what this looks like graphically. I am using perfect squares because when I take those values and plug them in for x I am going to square root them. Why not pick numbers that I can graph easily. I don't think I am going to use my x value of 16 in this small grid. We will go along with it anyway. If I plug in zero for x, I get the square root of zero is zero. Plugging in 4, I have the square root of four which is two. If I plug in nine, the square root of nine is equal to three. And not that I have room to graph an x value of 16, the square root of sixteen is four. So this is going to look like (0,0), over four and up two, over nine and up three. So 1,2,3,4,5,6,7,8,9 and up three. Here we have our parent function y equals the square root of x I don't want to do a t-table every time I draw a graph, at least not when I am working with graphs I am already familiar with. If I want to graph y equals the square root of x minus 2, This plus or minus. When you have a plus or minus at the end of your equation (usually) that is outside your function, in this case my function is the square root symbol, that is a vertical shift. If were plus two you would move the graph up, we have minus 2, so we will move the graph down. Each of these individual points I plotted a minute ago are going down two places because of this minus two. Now I can redraw my square root function shifted down two places. Again, plus or minus at the end of your equation (vertical shifts can be at the beginning) outside your function, that is a vertical shift. Now what if I wanted to make this graph, y equals the square root of x minus two. A minus outside your function is a vertical shift. Vertical shifts are either up or down. If you have a plus or minus inside your function, in this case my square root symbol, that is a movement left or right. With an x minus two inside our function, that is a shift (translation) to the right two places. Not to the left two places like you might think because its subtraction, but it is to the right 2 units. If I were to plug in say... Let's set up a t-table. If I attempted to use a list of generic values such as zero, like this graph that starts at zero, zero minus two is negative two. You cannot square root negative two. You cannot square root a negative number. Furthermore, you can only square root a positive number. If I put in a value of two, two minus two is zero and the square root of zero is zero. You see how this point is at (2,0) where it used to be at (0,0) We are going to go over here and plot (2,0) Now lets put in 6. Why would I want to put in...

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