Type the correct answer in the box. Use numerals instead of words. If necessary, use/ for the fraction bar.Function g is a transformation of the parent sine function, f ( x ) = sin ⁡ ( x ) g ( x ) = 1 3 sin ⁡ ( 2 x − 5 ) + 1The phase shift of function g is ?

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Type the correct answer in the box. Use numerals instead of words. If necessary, use/ for the fraction bar.Function g is a transformation of the parent sine function,   f  (  x  )  =  sin  ⁡  (  x  )  g  (  x  )  =      1    3    sin  ⁡  (  2  x  −  5  )  +  1The phase shift of function g is ?

kampmatis194 · Accepted Answer

For the transformed sine function:  g  (  x  )  =  A  sin  ⁡  (  B  (  x  −  C  )  )  +  DA=AmplitudeB=FrequencyC=Phase shift; If C&amp;gt;0   ⇒ Right shiftC &amp;lt; 0   ⇒ Left shiftD=Vertical shift; If D &amp;gt;0   ⇒ Upward shiftD&amp;lt;0   ⇒ Downward shiftHex,   g  (  x  )  =      1    3    sin  ⁡  (  2  x  −  5  )  +  1    =      1    3    ⋅  sin  ⁡  (  2  (  x  −      5    2    )  )  +  1Comparing with   g  (  x  )  =  A  sin  ⁡  (  B  (  x  −  C  )  )  +  D    A  =      1    3      B  =  2    C  =      5    2      D  =  1  ∴   Phase shift   =      5    2

Function g is a transformation of the parent sine function, f(x)=sin(x), g(x)=1/3 sin(2x-5)+1. The phase shift of function g is ?

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