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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):
- Left shift by c units: [tex]y = f(x+c)[/tex]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 = 0.35\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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