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
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 A, 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)
- Vertical shift:
- Up by d units:
- Down by d units:
- Stretching:
- 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:
