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# Shifting,-Reflecting,-and-Stretching-Graphs

last edited by 11 years, 7 months ago

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

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: