the table shows the average daily temperature on the first day of each month for one year. use the graphing…

the table shows the average daily temperature on the first day of each month for one year. use the graphing calculator to graph the data points. use 0 for january, 1 for february, 2 for march, and so on. the graph of these points follows a path resembling a cosine curve reflected across the y - axis sine curve reflected across the y - axis cosine curve reflected across the x - axis sine curve reflected across the x - axis

the table shows the average daily temperature on the first day of each month for one year. use the graphing calculator to graph the data points. use 0 for january, 1 for february, 2 for march, and so on. the graph of these points follows a path resembling a cosine curve reflected across the y - axis sine curve reflected across the y - axis cosine curve reflected across the x - axis sine curve reflected across the x - axis

Answer

Explanation:

Step1: Analyze the general shape of the data

The data shows a periodic pattern (temperature changes throughout the year). A cosine or sine curve is used for periodic functions.

Step2: Consider the reflection

A cosine curve (y = A\cos(Bx - C)+D) has a maximum at (x = 0) (if (C = 0)). The given data has a maximum in June (when (x = 5)). A cosine curve reflected across the (y -)axis ((y=A\cos(-Bx - C)+D=A\cos(Bx + C)+D)) can be adjusted (by choosing appropriate (B), (C), (D)) to fit the data. A sine curve (y = A\sin(Bx - C)+D) has a value of (y = D) at (x=\frac{C}{B}). The data does not match the initial - value property of a non - reflected or (x -)axis / (y -)axis reflected sine curve as closely as a (y -)axis reflected cosine curve.

Answer:

cosine curve reflected across the (y -)axis