To convert a temperature from degrees Celsius (C ) to degrees Fahrenheit (F ), we use the formula


F = (9⁄5)C + 32.

Outside of the United States, temperature readings are usually given in degrees Celsius. A rough approximation of the Fahrenheit equivalent for a Celsius reading can be found by doubling the Celsius reading and adding 32°.

1. Write a formula to calculate the Fahrenheit approximation, F , of a Celsius temperature, C .
   
   
2. For what range of Fahrenheit temperatures, if any, is the approximation less than (or greater than) the correctly calculated value?
   
   
3. For what temperature, if any, is the approximation the same as the correctly calculated temperature?
   
   

You can use the graphing calculator to help answer the questions.

• First create the algebraic equivalent of the approximation by "doubling and adding 32".
  
  
• Let "x" represent the Celsius temperature (the independent variable), and "y" represent the Fahrenheit temperature (the dependent variable). Enter the correct equation in for "Y₁", and enter the approximation equation in as "Y₂".
  
  
• Determine and enter appropriate values for the Window settings. Look at the graph to insure you are seeing enough of the important information in the graph.
  
  
• You can use the TRACE function to approximate the relative values of "Y₁" and "Y₂" for the same value of "x". Better yet, use
  2nd-CALC >> 5:intersect >> ENTER >> ENTER >> ENTER to let the calculator find the exact coordinates of the point of intersection.