Is It Done Yet
Is It Done Yet? Name______________________
Lab Sheet Period_____Date_____________
Using the candy thermometer handout, find 6 places where a Fahrenheit temperature aligns exactly with a Celsius temperature. Record the corresponding temperatures in the table below.
Graph the ordered pairs ((F, (C) on your calculator and
show the result below. Include your window settings.
Xmin=_______Xmax=_______
Ymin=_______Ymax=_______
Select two of these points and show work to write the equation of the line through these points in slope-intercept form. (Use the variables F and C instead of x and y.)
Many science classes are given a formula that relates Fahrenheit and Celsius degrees. Usually the formula is:
[pic] (A)
Explain why this formula doesn’t look like the equation you just got.
Show work to rewrite the formula in the box to solve for C.
(B)
Compare and contrast this formula with the equation you calculated using the two points.
The formula in the box is a function for degrees Fahrenheit in terms of degrees Celsius, and could be written [pic]. What is the domain of F(C)?
What is the range of F(C)?
Why don’t your data points lie on F(C)?
What could you do to your data (ordered pairs) to make the points lie on F(C)?
Plot both sets of points on your calculator, along with the lines represented by equations (A) and (B). Use the window given below, and copy your graph below.
Xmin = 0 Xmax = 600
Ymin = 0 Ymax = 400
These equations are called inverses of
each other, because one maps (F to (C,
and the other maps (C to (F.
Now plot the line y = x on the above graph. With that in mind, where do you see reflection occurring with these three lines?
The ordered pair (0, 32) lies on one of these lines. Which one?
What does that mean in terms of degrees Celsius and degrees Fahrenheit?
Use this reflection to find the inverse of (0, 32).____________ Show algebraically that this inverse satisfies the other equation.
Evaluate: F(10) = _____ F(85) = ______C(18)? = ______C(56) = _______.
What is the value of F(C(27))?______What is the value of C(F(50))?______
Explain why we get these results.
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|Degree in Fahrenheit |Degree in Celsius |
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[pic]
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