Respuesta :
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]\dfrac{\pi}{4}[/tex]
- phase shift of [tex]\dfrac{\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]A, assuming horizontal axis is input axis and vertical is for outputs, then:
- Horizontal shift (also called phase shift):[tex]y=f(x+c)[/tex]
- Left shift by c units: earlier)
- Right shift by c units: [tex]y=f(x-c)[/tex] output, but c units late)
- Vertical shift:
- Up by d units: [tex]y=f(x)+d[/tex]
- Down by d units: [tex]y=f(x)-d[/tex]
- Stretching:
- Vertical stretch by a factor k: [tex]y=k\times f(x)[/tex]
- 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=0.35cos(8(x-\pi/4)[/tex]
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
[tex]\dfrac{2\pi}{8}=\dfrac{\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 (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
