Which of the following is true? there is a phase shift to the left. there is a phase shift to the right. the graph is reflected across the x-axis the graph is stretched horizontally. the graph is compressed horizontally.

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:

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