Question

The Sine Function

According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:

To get a feel for the relationship between the month and the average high temperatures, the data is plotted on the following scatter plot.

If the plot was extended to a two year period with 1 = Jan of the first year, 12 = Dec of the first year, 13 = Jan of the second year, 24 = Dec of the second year, describe the plot with the additional information.

a. Linear
b. Random dots
c. Wave-like and repetitive
d. Quadratic

Please select the best answer from the choices provided

Answer 1

C. Wave-like and repetitive

Explanation:

I calculated it logically

Answer 2

The most accurate way to describe the plot with the additional information is as wave-like and repetitive.

The scatter plot shows a clear wave-like pattern, with high temperatures peaking in the summer months (July and August) and dropping in the winter months (December and January).

This pattern repeats itself over the two-year period, suggesting that the average monthly high temperature in Dallas/Fort Worth is influenced by seasonal changes.

A linear function would not be able to capture this wave-like pattern, as it would only produce a straight line. A quadratic function might be able to approximate the pattern, but it would not be as accurate as a sine function, which is specifically designed to model periodic phenomena.

Therefore, the most accurate way to describe the plot with the additional information is as wave-like and repetitive.