Answer :
To answer the question of which term gives the number of cycles of a periodic function that occur in one horizontal unit, we need to understand a few key concepts in the study of periodic functions.
1. Period: The period of a periodic function is the length of one complete cycle. It is a measure of the distance over which the function repeats itself. For example, for the sine function [tex]\( \sin(x) \)[/tex], the period is [tex]\( 2\pi \)[/tex].
2. Frequency: The frequency of a periodic function is the number of cycles that the function completes within a unit interval on the horizontal axis. It is essentially the reciprocal of the period. Mathematically, if [tex]\( T \)[/tex] is the period, then the frequency [tex]\( f \)[/tex] is given by [tex]\( f = \frac{1}{T} \)[/tex].
3. Vertical Shift: This term refers to the displacement of the function's graph up or down along the vertical axis. It does not affect the number of cycles within a unit horizontal distance.
Given these definitions, the term that specifically describes the number of cycles of a periodic function that occur in one horizontal unit is frequency.
Therefore, the answer is:
- Frequency
1. Period: The period of a periodic function is the length of one complete cycle. It is a measure of the distance over which the function repeats itself. For example, for the sine function [tex]\( \sin(x) \)[/tex], the period is [tex]\( 2\pi \)[/tex].
2. Frequency: The frequency of a periodic function is the number of cycles that the function completes within a unit interval on the horizontal axis. It is essentially the reciprocal of the period. Mathematically, if [tex]\( T \)[/tex] is the period, then the frequency [tex]\( f \)[/tex] is given by [tex]\( f = \frac{1}{T} \)[/tex].
3. Vertical Shift: This term refers to the displacement of the function's graph up or down along the vertical axis. It does not affect the number of cycles within a unit horizontal distance.
Given these definitions, the term that specifically describes the number of cycles of a periodic function that occur in one horizontal unit is frequency.
Therefore, the answer is:
- Frequency
