Which transformations are needed to change the parent cosine function to y = 0. 35 cosine (8 (x minus StartFraction pi Over 4 EndFraction))? vertical stretch of 0. 35, horizontal stretch to a period of 16 pi, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical compression of 0. 35, horizontal compression to a period of 4 pi, phase shift of StartFraction pi Over 4 EndFraction units to the left vertical compression of 0. 35, horizontal compression to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right vertical stretch of 0. 35, horizontal stretch to a period of StartFraction pi Over 4 EndFraction, phase shift of StartFraction pi Over 4 EndFraction units to the right.

The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is , assuming horizontal axis is input axis and vertical is for outputs, then:

For this case, we're specified that:

y = cos(x) (the parent cosine function) was transformed to

We can see its vertical stretch by 0.35, right shift by horizontal stretch by 1/8

Period of cos(x) is of length. But 1.8 stretching makes its period shrink to

Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:

Learn more about transformation of functions here:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt