Graphing Trigonometric Functions with Translations and Asymptotes
Key Questions

The amplitude is the distance from the midline to the maximum or to the minimum (they are the same). For example,
#y = sin(x)# has an amplitude of 1 because the midline is#y=0# and the max is 1.This can be found by finding the range of the function and dividing by two. (See if you can figure out why.)


By changing the "c" in your basic trigonometric equation.
The standard trig equation for sine is
#y=a*sin[b(xcpi)]+d# . In this, the variable#a# represents the amplitude. The variable#b# represents the period (#(2pi)/b# = period). Now, the variable#c# represents what is known as the phase shift  more commonly known as a horizontal translation. You shift the graph#cpi# units from the original parent function, which in this case is#y=sinx# . If#c# is positive, shift the graph to the right#cpi# unites. If#c# is negative, shift the graph to the left#cpi# units.If you're wondering,
#d# represents the vertical translation.I hope this helps, and I'f strongly suggest going to google and typing in functions like
#y=sin(x2pi)# and comparing them to the parent function,#y=sinx# .