Graph the following function by applying transformation to f(x) = sin x. State the amplitude, period, phase shift, and vertical shift.

Question

Graph the function  by applying transformation to f(x) = sin x.

State the amplitude, period, phase shift, and vertical shift.

Please show all work in a neat and organized manner. Thank you! :D

Answer 1

vertical shift = 1.5

phase shift = 80 degrees

amplitude shift or stretch = 3.5

period reduction = 1/5 or frequency increase = 5

period of sinx = 2pi

period of 3.5(sin5x + 80) + 1.5 has period of 1/5(2pi) = 2pi/5

frequency of 3.5(sin5x + 80) +1.5 has frequency 5/2pi

genreal formula is

f(x) = A(sinBx + C) +D

where D is the vertical shift

A is the amplitude stretch or compression

C is the phase shift

and B is related to the period or frequency

if B = 1, period = 2pi

if B =5 period = 2pi/5

period = 2pi/B

frequency = B/2pi

take the sinx graph and move it up 1.5. the new midline is now y=1.5, no longer the x axis

stretch it verticallly by a factor of 3.5. New maximum is now 3.5+1.5 = 5

and new minimum is now 3.5 -1.5 = 2

, and compress it horizontally by a factor of 5, like compressing a spring to make the springs closer together, 5 times closer

then horizontally shift the curve 80 degrees