On a spring day in Boston, MA, the temperature was recorded every hour over the course of the day. The graph shows the relationship between the temperature in Boston and the time of day in hours since midnight.

Question

Based on the graph, is time a function of temperature?
Time
a function of temperature because
.
x
y
0
5
10
15
20
25
0
4
8
12
16
20
24
Temperature (°C)
Time (hr)

Answer 1

To determine if time is a function of temperature based on the graph you described, we need to understand the definition of a function. A relationship is a function if every input (in this case, temperature) corresponds to exactly one output (in this case, time).

In your scenario, if the graph shows that for each temperature value, there is only one corresponding time value, then yes, time is a function of temperature. However, if the graph shows that multiple time values correspond to the same temperature value (for example, if the temperature at 12:00 PM and 6:00 PM is the same), then time is not a function of temperature.

Since I can't see the graph, I suggest you look for these key points:

1. Unique Mapping: Check if for every temperature on the vertical axis, there is only one point on the horizontal axis.
2. Multiple Values: If any temperature corresponds to multiple times, then time is not a function of temperature.

So, your conclusion can be phrased as follows:

• If time is a function of temperature: "Time is a function of temperature because each temperature corresponds to exactly one time of day."

• If time is not a function of temperature: "Time is not a function of temperature because the same temperature corresponds to multiple times of day."

By analyzing the graph with these criteria, you should be able to conclude whether time is a function of temperature.