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Sagot :
Answer:
a. There is a phase shift to the left
Step-by-step explanation:
The correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
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), 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]output, but c units earlier)
- Right shift by c units: [tex]y=f(x-c)[/tex] (same output, but c units late)
Vertical shift:
- Up by d units: f(x) + d
- Down by d units: y = f(x) - d
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, the parent function y = cos(x) is transformed to make the function y = cos (x + pi/6)
Thus, there is left shift of the graph of the function y =cos(x).
The graphs of both functions (parent function in red color and transformed function in blue color) is given below.
Thus, the correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
Learn more about transforming functions here:
https://brainly.com/question/17006186
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