The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.

Question

What is the equation of the new function  g(x) ?

 

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g(x)= 

Answer 1

ƒ(x)=sin(x)

consider y = Asin(Bx + C)+D

A controls the amplitude (how high/low the function is)

B controls the # of complete wavelengths in a specified interval

C is the phase shift (left/right on the axis) -- (positive values will shift left)

D is the vertical shift (up/down) ex. +3 would move the whole function UP 3 units

In your case you want to stretch vertically -- that is the amplitude so A=4

And since you want to shift it 3 units right C = -3 (always the opposite of the direction you want to go)

Put it together...

g(x) = 4sin(x - 3)

Answer 2

To strech the function vertically by a factor of 4, multiply it with 4.

To shift the function 3 units to the right, replace x with x - 3.

g(x) = 4sin(x - 3)