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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

Sagot :

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

  • vertical stretch of 0.35
  • horizontal compression of period of [tex]\pi/4[/tex]
  • phase shift of [tex]\pi/4[/tex] to right

How does transformation of a function happens?

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 [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:

  • Horizontal shift (also called phase shift):
  1. Left shift by c units: [tex]y = f(x+c)[/tex]earlier)
  2. Right shift by c units: [tex]y = f(x-c)[/tex]output, but c units late)
  • Vertical shift:
  1. Up by d units: [tex]y = f(x) + d[/tex]
  2. Down by d units: [tex]y = f(x) - d[/tex]
  • Stretching:
  1. Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]
  2. Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]

For this case, we're specified that:

y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]

We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8

Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]

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

  • vertical stretch of 0.35
  • horizontal compression to period of [tex]\pi/4[/tex] (which means period of cosine is shrunk to [tex]\pi/4[/tex] which originally was [tex]2\pi[/tex] )
  • phase shift of [tex]\pi/4[/tex] to right

Learn more about transformation of functions here:

https://brainly.com/question/17006186

Answer: 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

Step-by-step explanation:

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