During the winter, you program your home thermostat so that at midnight, the temperature is 55°. This temperature is maintained until 6 A.M. Then the house begins to warm up so that by 9 A.M. the temperature is 65°. At 6 P.M. the house begins to cool. By 9 P.M., the temperature is again 55°. The graph (as attached herewith) illustrates home temperature, f(t), as a function of hours after midnight, t.
Using the given graph determine whether the below given statement makes sense or does not make sense, and explain your reasoning. If the statement makes sense, graph the new function on the domain [0, 24]. If the statement does not make sense, correct the function in the statement and graph the corrected function on the domain [0, 24].
"I decided to keep the house 5° warmer than before, so I reprogrammed the thermostat to y = f(t) + 5."
GIven,
To keep the house 5° warmer, the thermostat was reprogrammed as
y= f(t) +5
let the thermostat follow the equation
y= f(t)
where
y is a function of t
t is time in hours
and f(t) is the temperature in degrees.
to keep the house 50 warmer than before.
the function f(t) shifts 5 degrees upward in the y-axis.
Thus the reprogrammed equation is
y= f(t) +5
or 50 is added to each y corrdinate.
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