Writing an Equation of a Transformed Function Graph

Hi! The name is Raphael. Thats R to the A to the P.H.A.E.L. 

Aight, so last friday, we talked about Writing an Equation of a Transformed Function Graph. This part, I believe, is the most simple part of unit II.

  

As you can see from the picture above, the left part of the graph , y=g(x) , represents a transformation of the graph on the right, which is y=f(x). On this example, it says; Determine the equation of g(x) in the form y=af(b(x-h))+k.

In order to find the values of a, b, h and k, you must do the following: 

                      For k, the y-values are affected. which means it can go "up" or "down".

from the example above, in order to find k, you have to get the distance between the two middle points.

For h, the x-values are affected.

As you can see from the picture, the graph of y=f(x) was moved 7 units to the left. which means, the value of h is -7.

For a, y-values are also affected.

On the form y=af(b(x-h))+k, In order to get the y-values of y=g(x), you must multiply the y-values of

y=f(x) to a. To find a from the picture above, you must divide the lenght (vertically) of y=g(x) by the lenght

of y=f(x). In this case, the lenght of y=g(x) from bottom point to the top is 8, and the lenght of y=f(x) from top to bottom is 4. So that's 8/4 = 2.

 For b,  x-values are affected. 

In order to get the x-value of y=g(x), you must multiply the coordinates of y=f(x) by b. In order to find b from the example above, you will have to divide the distance of the two end points of  y=g(x) by the distance of the two end points of y=f(x). so that's 2/8= 1/4.  and ofcourse the reciprocal of 1/4 is 4.

Here are more examples:

THAT'S ALL FOLKS! :)