trig problem: please help w/ transformations of graphs

[MathisHard101]

Equation: parent function (pre-image) is y=cos(x)

Equation: image function is y= -2 cos 3(x-?) + 5

Explain how the graph of the image equation can be obtained from the graph of the parent function equation by applying the appropriate transformations?

 

[wjm11]

Equation: parent function (pre-image) is y=cos(x)

Equation: image function is y= -2 cos 3(x-?) + 5

Explain how the graph of the image equation can be obtained from the graph of the parent function equation by applying the appropriate transformations?

The 2 doubles the amplitude from 1 to 2.

The “-“ in front of the 2 flips/reflects the wave form about its longitudinal axis.

The “-pi” is called the phase shift. It shifts the wave form pi units to the right (an x translation).

The 3 changes the period from 2pi to 2pi/3.

The 5 is a y translation, moving the wave 5 units up.