Question

what is the phase shift of a periodic function?

○ a horizontal translation of the function

○ the horizontal length of one cycle of the function

○ the number of cycles of the function that occur in one horizontal unit

○ a vertical translation of the function

Explanation:

To determine the phase shift of a periodic function, we analyze each option:

• The first option: A phase shift in periodic functions (like trigonometric functions) is a horizontal translation. For example, in \( y = \sin(x - h) \), \( h \) represents the horizontal shift (phase shift) of the sine function.
• The second option: The horizontal length of one cycle is the period, not the phase shift.
• The third option: The number of cycles per horizontal unit is the frequency, not the phase shift.
• The fourth option: A vertical translation is a shift up or down, which is not related to phase shift (a horizontal concept for periodic functions).

So the correct description of phase shift is a horizontal translation of the function.

Answer:

a horizontal translation of the function