Which of the following statements best describes a trigonometric function having undergone a phase shift? Select all that apply.The graph of y = sec x is translated three units to the left.The graph of y = cot x is reflected over the horizontal axis.The graph of y = tan x is reflected over the vertical axis.The graph of y = sin x is translated three units down.The graph of y = csc x is translated three units to the right.The graph of y = cos x is translated three units up.

To describe a trigonometric function that has undergone a phase shift, we need to understand the effects of translation and reflection on the graph.

1. The statement "The graph of y = sec x is translated three units to the left" does not describe a phase shift. It describes a horizontal translation.

2. The statement "The graph of y = cot x is reflected over the horizontal axis" does describe a phase shift. When a function is reflected over the horizontal axis, it undergoes a phase shift of π radians.

3. The statement "The graph of y = tan x is reflected over the vertical axis" does not describe a phase shift. It describes a vertical reflection.

4. The statement "The graph of y = sin x is translated three units down" does describe a phase shift. When a function is translated vertically, it undergoes a phase shift.

5. The statement "The graph of y = csc x is translated three units to the right" does describe a phase shift. When a function is translated horizontally, it undergoes a phase shift.

6. The statement "The graph of y = cos x is translated three units up" does describe a phase shift. When a function is translated vertically, it undergoes a phase shift.

Therefore, the statements that best describe a trigonometric function having undergone a phase shift are:

• The graph of y = cot x is reflected over the horizontal axis.
• The graph of y = sin x is translated three units down.
• The graph of y = csc x is translated three units to the right.
• The graph of y = cos x is translated three units up.

To describe a trigonometric function that has undergone a phase shift, we need to understand the effects of translation and reflection on the graph.

1. The statement "The graph of y = sec x is translated three units to the left" does not describe a phase shift. It describes a horizontal translation.

2. The statement "The graph of y = cot x is reflected over the horizontal axis" does describe a phase shift. When a function is reflected over the horizontal axis, it undergoes a phase shift of π radians.

3. The statement "The graph of y = tan x is reflected over the vertical axis" does not describe a phase shift. It describes a vertical reflection.

4. The statement "The graph of y = sin x is translated three units down" does describe a phase shift. When a function is translated vertically, it undergoes a phase shift.

5. The statement "The graph of y = csc x is translated three units to the right" does describe a phase shift. When a function is translated horizontally, it undergoes a phase shift.

6. The statement "The graph of y = cos x is translated three units up" does describe a phase shift. When a function is translated vertically, it undergoes a phase shift.

Therefore, the statements that best describe a trigonometric function having undergone a phase shift are:

• The graph of y = cot x is reflected over the horizontal axis.
• The graph of y = sin x is translated three units down.
• The graph of y = csc x is translated three units to the right.
• The graph of y = cos x is translated three units up.