SOLUTION: what is the amplitude, period, and phase shift of f(x)= -3sin(4x-pi)-5?

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Question 1156186: what is the amplitude, period, and phase shift of f(x)= -3sin(4x-pi)-5?
Found 3 solutions by Edwin McCravy, MathLover1, ikleyn:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

For  or 









Edwin
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

what is the amplitude, period, and phase shift of


where
= the amplitude
= the number of times the graph will repeat itself in the “normal” period, which is for sin
= the horizontal shift or phase shift of the graph, when is subtracted from , it shifts to the
= the vertical shift of the graph (up or down)
in your case:
amplitude:
period:
phase shift to the :
vertical shift: ( units down)

Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.

1)  Amplitude is ALWAYS positive value and NEVER is negative value, by the definition.


    So, in this problem the amplitude is |-3| = 3.


        NOT  -3  (!) (!) (!)




2)  The parent function to measure the shift in this problem  IS NOT -3sin(4x) - 5, as @Mathlover MISTAKENLY thinks 

     and determines the phase shift incorrectly.


    To determine the shift, the given function should be presented wit POSITIVE amplitude

        -3sn(4x-pi) - 5 = 3sin(4x) - 5

    which shows that the phase shift is 0 (zero, ZERO) in this case.


See the plot below.



    


    Plot y = -3*sin(4x-3.14) - 5


Thus regarding the amplitude and the phase shift, the answers by @MathLower1 are incorrect.


Edwin correctly found the amplitude as positive 3, but regarding the phase shift, he dodged a direct answer.



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