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
- phase shift of to right
<h3>How does transformation of a function happens?</h3>
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 , assuming horizontal axis is input axis and vertical is for outputs, then:
- Horizontal shift (also called phase shift):
- Left shift by c units: earlier)
- Right shift by c units: output, but c units late)
- Up by d units:
- Down by d units:
- Vertical stretch by a factor k:
- Horizontal stretch by a factor k:
For this case, we're specified that:
y = cos(x) (the parent cosine function) was transformed to
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
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