Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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:

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.