Web Activities

CHAPTER 3 FUNCTIONS TOOLKIT

The Scenario

In section 3.4, you investigated a rule of thumb that allowed you to convert between the temperature scales Fahrenheit and Celsius. While easy to use, the results only provide approximations.

In this activity, you'll investigate temperature functions, and determine the actual function that allows you to convert back and forth between the two most common temperature scales.

Investigating Temperature Functions

1. Use the Internet to determine and record today's temperatures of ten cities across Canada. Create a table similar to the one below to record the data. Ensure that you select cities from ten of the provinces and territories.

2. Create a scatterplot using Fahrenheit as the independent variable x, and Celsius as the dependent variable y.
   
   
3. Draw the line of best fit and determine the equation of the line. Is this relation a function? Explain.
   
   
4. Verify your results using linear regression and the TI-83 plus graphing calculator.
   
   
5. If temperatures are restricted to Canada, state a reasonable domain and range for this function.
   
   
6. a) Express the equation that you found using function notation where f denotes the function.
   b) Explain the significance of this function.
   c) Evaluate and explain the significance of f(32) and f(212).
   
   
7. a) Draw a graph of f -1(x). Is this relation a function? Explain.
   b) Find f -1(x).
   c) If temperatures are restricted to Canada, state a reasonable domain and range for this function.
   
   
8. Scientists also use a third temperature scale called the Kelvin Scale. Use the 10 values from your original table and the Temperature Conversion Calculator to complete two tables as follows:

9. Determine the functions that this calculator uses to convert:
   a) Fahrenheit temperatures to Kelvin
   b) Celsius temperatures to Kelvin
   c) Kelvin temperatures to Fahrenheit
   d) Kelvin temperatures to Celsius

Your Job

Create a report that includes the following items:

• your table, scatter plot and the line of best fit;
• your calculations used to determine the equation of the line of best fit;
• the linear regression equation you determined, including the correlation coefficient;
• an explanation of the significance of f(x) and f -1(x) in this situation;
• the domain and range of f(x) and f -1(x) in this situation;
• the calculations used to determine f -1(x);
• the functions used by the temperature conversion calculator followed by an explanation of how you determined these functions; and
• a brief history of each temperature scale and a discussion of how each are used.

Your report must be at least 500 words (approximately two double-spaced pages). You will be assessed on how well the report addresses the criteria listed above.