Standard For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. <span class='clarification'>Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.</span>

Warming and Cooling

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Alignments to Content Standards: F-IF.B.4

Student View

Task

The figure shows the graph of $T$ , the temperature (in degrees Fahrenheit) over one particular 20-hour period in Santa Elena as a function of time $t$.

Temperature_graph_62e255e21882a1a0ad0409f69f851370

Estimate $T(14)$.
If $t=0$ corresponds to midnight, interpret what we mean by $T(14)$ in words.
Estimate the highest temperature during this period from the graph.
When was the temperature decreasing?
If Anya wants to go for a two-hour hike and return before the temperature gets over 80 degrees, when should she leave?

IM Commentary

This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, $t=0$ is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.

Solution

$T(14)$ is a little less than 90 degrees Fahrenheit; maybe 88 or 89 degrees.
The temperature was almost 90 degrees at 2:00 in the afternoon.
The highest temperature was about 90 degrees.
The temperature was decreasing between 4:00 p.m. and 8:00 p.m. It might have continued to decrease after that, but there is no information about the temperature after 8:00 p.m.
The temperature reaches 80 degrees just before 10:00 a.m. If Anya wants to go for a two-hour hike and return before the temperature gets over 80 degrees, then she should start her hike before 8:00 a.m.