Rounded to the nearest hour, Los Angeles averages 14 hours...

Name: Problem 83, Chapter 4: Precalculus
Uploaded: 2020-04-04T22:27:52-08:00
Duration: 2 min 39 s
Channel: Monique Rousselle Maynard
Description: Rounded to the nearest hour, Los Angeles averages 14 hours of daylight in June, 10 hours in December, and 12 hours in March and September. Let x represent the number of months after June and let y represent the number of hours of daylight in month x. Make a graph that displays the information from June of one year to June of the following year.

Rounded to the nearest hour, Los Angeles averages 14 hours of daylight in June, 10 hours in December, and 12 hours in March and September. Let x represent the number of months after June and let y represent the number of hours of daylight in month x. Make a graph that displays the information from June of one year to June of the following year.

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Key Concepts

Modeling Seasonal Variations

Seasonal variations are naturally modeled using periodic functions due to their repeating behavior. This concept links mathematical modeling to real-life observations by capturing the smooth transitions of daylight hours throughout the year and conveying the underlying cyclical pattern.

Graphing Data Points

Graphing the data involves plotting key points based on the given information, such as (0, 14) for June, (3, 12) for March, (6, 10) for December, and (9, 12) for September. This process visualizes the seasonal changes and provides a tangible representation of the relationship between months and daylight hours.

Periodic Functions

Periodic functions repeat their values in regular intervals, making them ideal for modeling cyclical phenomena such as the change in daylight hours throughout the year. Recognizing that the daylight data follows a regular annual cycle helps in selecting appropriate mathematical models, like sine or cosine functions, to represent the pattern.

Domain and Range

Identifying the domain and range is crucial in graphing functions. In this context, the domain is defined as the number of months after June (from 0 to 12), representing one full cycle of the year, while the range corresponds to the daylight hours, which vary between approximately 10 and 14 hours.

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