Answer :
To determine whether the temperature in the oven is a function of time, we need to understand what a function is in mathematical terms. A function is a relationship where each input has exactly one output.
In this scenario, the input is the time, and the output is the oven's temperature. Let's analyze what happens during the given time period:
1. Preheating Phase (5:00 p.m. to 5:10 p.m.):
- The temperature increases from [tex]\(72^\circ F\)[/tex] to [tex]\(400^\circ F\)[/tex]. During these 10 minutes, for each moment in time, there is a distinct temperature as the oven is steadily heating up.
2. Heating Phase (5:10 p.m. to 5:55 p.m.):
- The temperature remains constant at [tex]\(400^\circ F\)[/tex] for 45 minutes. At any specific time during this period, the oven temperature is precisely [tex]\(400^\circ F\)[/tex].
3. Cooling Phase (5:55 p.m. to 6:55 p.m.):
- The temperature drops from [tex]\(400^\circ F\)[/tex] back to [tex]\(72^\circ F\)[/tex]. Again, for every moment during these 60 minutes, there is a unique temperature as the oven gradually cools down.
Throughout the entire period from 5:00 p.m. to 6:55 p.m., at every specific time, the oven has exactly one distinct temperature. This means that for every input (specific time), there is a single, unique output (oven temperature).
Thus, the relationship between time and oven temperature is a function. The best statement that explains this is:
"It is a function because at any given time the oven was exactly one temperature."
In this scenario, the input is the time, and the output is the oven's temperature. Let's analyze what happens during the given time period:
1. Preheating Phase (5:00 p.m. to 5:10 p.m.):
- The temperature increases from [tex]\(72^\circ F\)[/tex] to [tex]\(400^\circ F\)[/tex]. During these 10 minutes, for each moment in time, there is a distinct temperature as the oven is steadily heating up.
2. Heating Phase (5:10 p.m. to 5:55 p.m.):
- The temperature remains constant at [tex]\(400^\circ F\)[/tex] for 45 minutes. At any specific time during this period, the oven temperature is precisely [tex]\(400^\circ F\)[/tex].
3. Cooling Phase (5:55 p.m. to 6:55 p.m.):
- The temperature drops from [tex]\(400^\circ F\)[/tex] back to [tex]\(72^\circ F\)[/tex]. Again, for every moment during these 60 minutes, there is a unique temperature as the oven gradually cools down.
Throughout the entire period from 5:00 p.m. to 6:55 p.m., at every specific time, the oven has exactly one distinct temperature. This means that for every input (specific time), there is a single, unique output (oven temperature).
Thus, the relationship between time and oven temperature is a function. The best statement that explains this is:
"It is a function because at any given time the oven was exactly one temperature."
