Question

Which transformations are needed to change the parent cosine function to y = 0.35 cosine (8 (x minus startfraction pi over 4 endfraction))?

Answer 1

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 $\dfrac{\pi}{4}$
• phase shift of  $\dfrac{\pi}{4}$ 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 $y=f(x)$A, assuming horizontal axis is input axis and vertical is for outputs, then:

• Horizontal shift (also called phase shift):$y=f(x+c)$

1. Left shift by c units: earlier)
2. Right shift by c units: $y=f(x-c)$ output, but c units late)

• Vertical shift:

1. Up by d units: $y=f(x)+d$
2. Down by d units: $y=f(x)-d$

• Stretching:

1. Vertical stretch by a factor k: $y=k\times f(x)$
2. Horizontal stretch by a factor k: $y=f(\dfrac{x}{k})}$

For this case, we're specified that:

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

$y=0.35cos(8(x-\pi/4)$

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

$\dfrac{2\pi}{8}=\dfrac{\pi}{4}$

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  (which means period of cosine is shrunk to  which originally was  )

phase shift of  to right

Learn more about transformation of functions here:

brainly.com/question/17006186