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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
- 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.
| LOCATION |
TEMP (°F)
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TEMP (°C) |
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- Create a scatterplot using Fahrenheit as the independent variable
x, and Celsius as the dependent variable y.
- Draw the line of best fit and determine the equation of the
line. Is this relation a function? Explain.
- Verify your results using linear regression and the TI-83 plus
graphing calculator.
- If temperatures are restricted to Canada, state a reasonable
domain and range for this function.
- 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).
- 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.
- 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:
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| TEMP (°F)
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TEMP (°K)
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TEMP (°C) |
TEMP (°K)
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- 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.
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