Pre-Calc                                                          Notes 10/19

 

Translations!

 

Translations are simply moving a parent function to a new location on the coordinate grid.  The standard notation for a translation is: T(x,y): (x± h, y± k) where the positive values move the function to the right and up and where the negative values move the function to the left and down.  Each point on the parent graph is moved to the new location through the translation.  For instance, take the points (-4, 7), (1,3), (4, -8), and (-10, 2) and translate them by the translation  T(x,y): (x + 7, y – 8) __________________________________

(Note: you have studied these in geometry and algebra II so this should be a review)

 

Now, what gets a bit confusing is that when you write an equation with a translation, the signs of the x’s are opposite of what the translation is.  For instance, for a translation of

T(x,y): (x + 2, y – 3) in a quadratic, the equation becomes y = (x – 2)2 – 3.  For a cubic:

Y = (x – 2)3 – 3, for an inverse variation: ­   1       - 3 , and an inverse square:     1      - 3,

                                                             (x – 2)                                          (x – 2)2

also an absolute value: |x – 2| - 3, etc.

 

You also have to be careful about using plenty of parentheses to make sure the graph is correct on your calculator.

 

Now for the “What’s My Equation Game”  (Whom ever gets all the questions correct, wins the prize!!!!!!!!!!!!!!!!!!!!)

 

1)      For the following translations and parent functions, you are to write the equation of the translated function and sketch the graph:

 

a) T(x,y): (x + 2, y – 1)      b) T(x,y): (x -4, y – 3)          c) T(x,y): (x + 7, y + 2)             d) T(x,y): (x - 1, y +5)

            y = |x|                          y = Öx                                       y = 1/ x                                                y = x4

 

                       

 

 

_________________      _________________          _________________              __________________

 

 

 

 

 

2) For the next  portion of our “Equation Game”, you, the contestants, are to look at the graph I have on the screen and carefully sketch the graph, state the parent function, the translation, and the equation:

 

a)                                             b)                                             c)                                     d)

                               

 

__________________            ___________________          __________________     _________________

 

__________________            ___________________          __________________     _________________

 

__________________            ___________________          __________________     _________________

 

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