Which Transformations Are Needed To Change The Parent Cosine Function To Mc020-1.jpg?

A phase shift horizontal translation to the right.

Stride-by-step explanation:

A periodic function that does not start at the sinusoidal axis or at a maximum or a minimum has been shifted horizontally. This horizontal motility allows for different starting points since a cosine moving ridge does non have a beginning or an end.

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

So to alter the parent cosine role to the cosine function above, A stage shift horizontal translation to the right must have been done.

Step-by-step caption:

Question:

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

ii. vertical compression of ii, horizontal stretch to a menses of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the left, vertical shift of ii units downwards

3. vertical compression of 2, horizontal compression to a menses of 4 pi, phase shift of StartFraction pi Over iii EndFraction units to the left, vertical shift of 1 unit down

4. vertical stretch of two, horizontal compression to a menstruation of StartFraction pi Over ii EndFraction, phase shift of Pi units to the correct, vertical shift of 1 unit downwards

The correct option is;

4. Vertical stretch of 2, horizontal compression to a period of π/2, stage shift of π units to the right, vertical shift of ane unit downwardly

Step-by-step caption:

Hither, we have the parent cosine function given past y = cos(x)

A plot of the above part is attached

By comparing, it is observed that the transformation required to modify the parent function includes;

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

2. A horizontal compression so that the period of one complete revolution is π/two rather than 2·π in the parent cosine role

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

4. Shift of the y values from the symmetrical ten-centrality origin downward by 1 unit such that the maximum y value of the doubly stretched transformation is 1 rather than ii

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

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

Footstep-by-step explanation:

If you stretch cosine function past a factor of two, maximum volition be y = two and minimum will be y = -2, and after that you shift it 1 unit downwards maximum volition exist y = 1 and minimum will exist y = -3