Precalculus Help!

Question

You have been asked to write a function to predict the temperature based on the day of the year. You use the function t (d), where d represents the day of the year, and t (d) represents the temperature of the day in Celcius. As accurate as you could make it, it just wasn't enough. You were asked to change it to be a prediction by month instead of day. You were also asked to change it to be in Farenheit instead of Celcius.

Answer these questions in the discussion:

1. How would you update your function to show this?
2. How would the graph transform?
3. Explain your reasoning.

Answer 1

1) You would increase the frequency of the wave function you are using and modify both amplitude and vertical shift.

2) The period of the wave would decrease, the amplitude would increase, and the graph would shift upwards.

3) Imagine d on the x-axis of a graph and t(d) on the y. A complete yearly temperature change cycle would occur over x={0,365} if you are modeling on a daily basis. This means that if the temperature needs to be predicted monthly, that same cycle of temperature change now must cover x={0,12}. That yearly cycle must be squeezed down into the {0,12} interval and that can be accomplished by increasing the frequency. Amplitude and vertical shift must be altered to compensate for the change from Celsius to Fahrenheit. A span of -7 degrees C to 38 degrees C is equivalent to a span of 20 degrees F to 100 degrees F. The Fahrenheit scale covers a greater range (necessitating greater amplitude) and is also greater in value (necessitating a vertical shift upwards).