Hello , so my problem is :

Question

Let f(t) represent the temperature of a turkey baking in an oven as a function of time t in the oven (in minutes). This means time is the independent variable and temperature of the turkey is the dependent variable. The turkey was in the oven for 360 minutes and then removed. Note that when something is baked in an oven, the temperature of the oven stays constant.

Explain the meaning of each statement in the context of the situation using everyday language.

 

1. f(0) = 50

 

2. f(120) > f(60)

 

3. f(360) = f(345)

 

4. f(390) < f(360)

Answer 1

Hey Nat,

If you were to graph this function you would have t = time on the horizontal axis and f(t) = Temperature on the vertical axis. The temperature of the turkey DEPENDS ON, or is a function of, how much time it spends in the oven. And the more time it spends the hotter it gets, until perhaps the turkey reaches a peak temperature or the oven is turned off, which we are told is after 360 minutes.

f("some time") = "some Temperature" indicates that the point (some time, some Temperature) is on the graph of this function. An example would be f(10) = 70. This means that after 10 minutes in the oven, the turkey's temperature is 70 degrees.

1. f(0) = 50 - following the example above, this means that after 0 minutes in the oven, the turkey's temperature is 50 degrees or that the point (0, 50) is on the graph. This represents the y-intercept of this function since t=0. What does 0 minutes in the oven represent? It represents the temperature when I put the turkey in, which in this case is 50 degrees (maybe it was in the fridge and has been sitting out for a bit).
2. f(120) > f(60) - here, f(60) represents the turkey's temperature (not given) after it has been in the oven for 60 minutes. f(120) represents the turkey's temperature (not given) after it has been in the oven for 120 minutes. So this INEQUALITY states that the turkey's temperature after being in the oven for 120 minutes is GREATER THAN the turkey's temperature after being in the oven for 60 minutes.
3. f(360) = f(345) - here, f(345) represents the turkey's temperature (not given) after it has been in the oven for 345 minutes. f(360) represents the turkey's temperature (not given) after it has been in the oven for 360 minutes. So this EQUATION states that the turkey's temperature after being in the oven for 345 minutes is EQUAL TO (or the same) the turkey's temperature after being in the oven for 360 minutes.
4. f(390) < f(360) - here, f(360) represents the the turkey's temperature (not given) after it has been in the oven for 360 minutes, when we know it is removed from the oven. Since the turkey is removed after 360 minutes, f(390) represents the turkey's temperature (not given) after it has been OUT of the oven for 30 (390 - 360) minutes. So this INEQUALITY states that the turkey's temperature after being out of the oven for 30 minutes is LESS THAN the turkey's temperature after being in the oven for the full 360 minutes. This makes sense, as the turkey would begin to cool down after I remove it from the oven.

I hope this helps!! :)

Answer 2

We need to understand function notation when answering these questions. f(x)=y

For f(0)=50, the independent variable (x) is 0. The dependent variable is 50. In context, this means when the turkey is placed in the oven (cooked for 0 minutes) its temperature is 50 degrees.

I'll bet you can figure out the rest from there, but let's look at the second statement:

f(120)>f(60)

Which means the temperature of the turkey after 120 minutes is greater than the temperature of the turkey after 60 minutes. That makes sense because if the turkey is being cooked at a constant rate, it would be warmer the longer it is in the oven.

f(360) = f(345)

The temperature of the turkey did not change between 345 and 360 minutes of cook time.

f(390) < f(360)

At 390 minutes, the turkey temperature is less than it was at 360 minutes. Again, that makes sense because it was taken out of the oven after 360 minutes, and it would naturally begin to cool down at that point.