Which Transformations Are Needed To Change The Parent Sine Function To The Sine Function Below?

A phase shift horizontal translation to the right.

Step-by-pace explanation:

A periodic role that does not start at the sinusoidal axis or at a maximum or a minimum has been shifted horizontally. This horizontal movement allows for different starting points since a cosine wave does non take a beginning or an finish.

In this question, the sinusoidal wave is a cosine role of F(x) = cos x.

So to change the parent cosine function to the cosine part above, A stage shift horizontal translation to the correct must have been washed.

Step-by-step explanation:

Question:

ane. vertical stretch of two, horizontal stretch to a flow of ii pi, stage shift of StartFraction pi Over 2 EndFraction units to the right, vertical shift of one unit of measurement up

2. vertical compression of ii, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over four EndFraction units to the left, vertical shift of ii units down

3. vertical compression of two, horizontal compression to a period of iv pi, phase shift of StartFraction pi Over 3 EndFraction units to the left, vertical shift of one unit down

iv. vertical stretch of 2, horizontal compression to a catamenia of StartFraction pi Over 2 EndFraction, stage shift of Pi units to the right, vertical shift of i unit of measurement down

The right selection is;

4. Vertical stretch of 2, horizontal compression to a menstruation of π/ii, phase shift of π units to the correct, vertical shift of 1 unit down

Pace-by-footstep explanation:

Here, nosotros have the parent cosine role given past y = cos(ten)

A plot of the above function is attached

Past comparison, it is observed that the transformation required to change the parent function includes;

1. Vertical stretch from the parent function of amplitude 1 to amplitude 2

ii. A horizontal compression and then that the menstruation of one complete revolution is π/2 rather than ii·π in the parent cosine function

3. Stage shift of pi units to the correct such that cos(π) = ane rather than cos(2π) = 1 as it applies to the parent function

iv. Shift of the y values from the symmetrical ten-axis origin downwardly past 1 unit of measurement such that the maximum y value of the doubly stretched transformation is 1 rather than 2

Which transformations are needed to change the parent cosine function to the cosine function below?

vertical stretch of 2, horizontal pinch to a period of StartFraction pi Over two EndFraction, stage shift of Pi units to the right, vertical shift of 1 unit down

Pace-past-step caption:

If you stretch cosine function by a factor of 2, maximum will be y = 2 and minimum volition be y = -2, and after that you shift it ane unit of measurement down maximum will be y = one and minimum volition be y = -iii