How to write the Equation of a Transformed Graph

Bonjour tout le monde! :)

This is Vera, (btw it's VEH-RA not VEE-RA) and I sit in the front table between Allen & Macy and across Jim & Maye. 

          Last Friday we had our Unit Test about Permutations, Combinations and Binomal Theorem and hopefully we'll get the results tomorrow... 

          Also, we learned  "How to Write the Equation of a Transformed Graph" 

Here's an example:

 Absolute Value Function

                  To determine the equation of the of the g(x):

• First, let us write down the coordinates of the f(x) function:

                     y = f(x)                

                      (1, 1)          

                      (2,2)            

                      (3,3)           

                      (-1,1)              

                      (-2,2)      

•      Next, is to determine first if there are reflections, stretches and translations. 

                    

• If we look closely in the graph of g(x) we could see that there are no reflections and there are no translations because the graph did not move to the left or right, and up or down. so the only transformation we have in this graph are stretches.

• We could see that the graph was compressed vertically by a factor of (a) which is 3 units, meaning that the x- values will be multiplied by the reciprocal of 3 which is 1/3.

                                                 y = a f (b(x + c)) + d

                                                                Let us substitute 3 in to the equation

                                  y = a f (3(x + c)) + d

• Since there are no other transformations in this graph the final equation will be: g(x) = 3|x|
• Using mapping notation we could get all the y-values of the function g(x)= 3|x| by multiplying all the y-values of the function f(x) by 1/3.
• All x-values remain the same!

                      f(x)                                        = g(x)

                       y values                                   x, y

                      (1 x 1/3 = 3)                          = (1,3)

                      (2 x 1/3 = 6)                          = (2,6)

                      (3 x 1/3 = 9)                          = ( 3,9)    

                      (1 x 1/3 = 3)                         =  (-1,3)        

                      (2 x 1/3 = 6)                         =  (-2,6)

If you look closely, the coordinates we got from our equation was exactly the same as the points in the given graph, therefore our equation is correct!

That's how you get write an equation from a given graph! I hope you'll learn something. :) 

TBH: I don't get this topic as much as the other topics we had and I'm very unlucky to write about a topic I don't understand really well :< 

THAT'S ALL FOLKS! 

VERA,