How can we translate the graph of A to match one of the other graphs?

Remember the bakery with the thermostat set to ? At 5:00 a.m., the temperature in the kitchen rises to due to the ovens and other kitchen equipment being used until they are turned off at 10:00 a.m. When the owner decided to open 2 hours earlier, the baking schedule changed to match.

1. Andre thinks, “When the bakery starts baking 2 hours earlier, that means I need to subtract 2 from and that .” How could you help Andre understand the error in his thinking?
2. The graph of shows the temperatures after a change to the thermostat settings. What did the owner do?

   

   Graph of function . Horizontal axis, hours after midnight, scale 0 to 24 by 2’s. Vertical axis, degrees Fahrenheit, scale 50 to 100 by 10’s. Function starts at (0 comma 70) and is horizontal to (6 comma 70), then rises to (7 comma 90) and is horizontal to (11 comma 90). The function then drops to (12 comma 70) and is horizontal to (24 comma 70).

3. Write an expression for in terms of the original baking schedule, .

A piece of meat is taken out of the freezer to thaw. The data points show its temperature , in degrees Fahrenheit, hours after it was taken out. The graph , where , models the shape of the data but is in the wrong position.

0	13.1
0.41	22.9
1.84	29
2.37	36.1
2.95	36.8
3.53	38.8
3.74	40
4.17	42.2
4.92	45.8

Coordinate plane. Horizontal axis, t, hours, from 0 to 10 by 5’s. Vertical axis, M, degrees Fahrenheit, from negative 60 to 60 by 20’s. 9 data points plotted at 0 comma 13 point 1, 0 point 41 comma 22 point 9, 1 point 84 comma 29, 2 point 37 comma 36 point 1, 2 point 95 comma 36 point 8, 3 point 53 comma 38 point 8, 3 point 74 comma 40, 4 point 17 comma 42 point 2, 4 point 92 comma 45 point 8. Function moving upwards and to the right passing through negative 62 comma 0, 5 comma negative 27, and 10 comma negative 12.

Jada thinks changing the equation to makes a good model for the data. Noah thinks is better.

1. Without graphing, describe how Jada and Noah each transformed the graph of  to make their new functions to fit the data.
2. Use technology to graph the data,  and , on the same axes.
3. Whose function do you think best fits the data? Be prepared to explain your reasoning.