Sunday, January 22, 2012

Sinusoidol Functions:Transformations

This is another brief post for my exam studying.

Like most other kinds of functions, sinusoidal functions can can have transformations applied on their graphs:
f(x) = a sin (k(x-d))+ c

a is the vertical stretch and/or reflection. |a| is the amplitude.
k is the horizontal stretch and/or reflection, and it affects the period of the function. The period is |360÷k|
d is the horizontal translation. It doesn't affect the properties of the function
c is the vertical translation, and it determines what the equation of the axis is: the equation of axis is y=c

Also, using a and c, one can find the maximum and minimum points on the graph:
  • maximum value= c+ |a|
  • minimum value = c- |a|