Sure, let's break down the given question and understand the concepts to find the correct answer.
### Step-by-Step Solution:
1. Understanding Key Terms:
- Vertical Shift: This refers to the upward or downward displacement of a periodic function on a graph. It does not affect the number of cycles in a horizontal unit.
- Period: The period of a periodic function is the length of one complete cycle. For example, in the sine function [tex]\(y = \sin(x)\)[/tex], the period is [tex]\(2\pi\)[/tex].
- Frequency: Frequency is defined as the number of cycles a periodic function completes in one unit of time or space. It is the reciprocal of the period. For example, if a function has a period of [tex]\(2\pi\)[/tex], its frequency is [tex]\(\frac{1}{2\pi}\)[/tex].
- Phase Shift: This describes the horizontal shift left or right for a periodic function. It does not affect the number of cycles in a horizontal unit.
2. Analyzing the Question:
The question specifically asks: "Which term gives the number of cycles of a periodic function that occur in one horizontal unit?"
3. Evaluating Each Term:
- Vertical Shift: Does not relate to the number of cycles in a horizontal unit.
- Period: Defines the length of one cycle but not the number of cycles in one horizontal unit.
- Frequency: This is the term that directly relates to the number of cycles occurring in one horizontal unit. The higher the frequency, the more cycles occur in a given interval.
- Phase Shift: Refers to horizontal displacement but does not affect the number of cycles per horizontal unit.
4. Conclusion:
The term that accurately describes the number of cycles of a periodic function that occur in one horizontal unit is Frequency.
Therefore, the answer is:
Frequency
