6 Common Parent Functions

         f (x) = c                          f (x) = x                       f (x) = |x|

                Constant                        Linear                    Absolute Value

              f (x) = x^(1/2)                       f (x) = x^2                    f (x) = x^3

              Square Root                   Quadratic                      Cubic

For more parent functions go to:

http://itech.pjc.edu/falzone/handouts/parent_functions.pdf

Transformations can be Rigid or Nonrigid.

Rigid – change in position (translation/ reflection)

Nonrigid – change in shape of graph (stretch/ shrink)

Translations

Vertical:           f (x) +/-C           +C = up

- C = down

         Horizontal:      f (x +/- C)          +C = left

- C = right

ex. Describe the translation of the parent function f (x) = x^2

         a.)     f (x) = x^2 + 3            b.)    f (x) = (x – 1)^2 + 2

                         UP 3                                   RIGHT 1, UP 2

ex. Give the equation of the graph below

          f (x) = - | x – 2 | + 5

Reflections

        -f (x)   à           reflection over x-axis

          f (-x)  à           reflection over y-axis

ex. Reflect f (x) = x^3, over x-axis, right 4, up 3 and Graph.

    f (x) = - ( x – 4 )^3 + 3   

Stretch / Shrink      à Vertical,  cf (x)

         If   C > 1, then stretch (tall and skinny)

         If   0 < C < 1, (short and fat)

ex.   -5x^2

          -5x^2   reflect x-axis, stretch 5

ex.   -1/3f ( x + 6 ) – 5

          -1/3f ( x + 6 ) – 5 reflect x-axis, shrink 1/3, left 6, down 5

To graph these equations on the computer you can use the web site:

http://gcalc.net/

For further understanding check out this video:

http://video.google.com/videoplay?docid=6688242598665049815&ei=kj9IScf-JpPuqAKj4KH8BQ&q=Shifting%2CReflecting%2C+and+Stretching-Graphs