List the transformation(s) from f(x) to g(x)

Question

f(x)=sin x
g(x)=5sin(x-(pi)/2)

 

f(x)=cos x 

g(x)=-cos(x)+3

Answer 1

 

FIRST 2 FUNCTIONS:

 

    g(x) is shifted to the right by pi/2 as a result of pi/2 subtracted from the angle

    g(x)'s wave is taller ... amplitude of 5, in comparison to an amplitude of 1 for f(x) ... as a result of the 5 that precedes the sin function

 

SECOND 3 FUNCTIONS:

 

     g(x) is reflected across the x-axis as a result of the negative that precedes the cos function

     g(x) is shifted up 3 units as a result of the 3 added to the entire function value