Warm Up
Examine the following 4 graphs and think about why 1 of the graphs does not belong in the same group as the other 3.
Graph A
Graph B
Graph C
Graph D
Examine the following 4 graphs and think about why 1 of the graphs does not belong in the same group as the other 3. Which graph do you think does not belong in a group with the other 3 graphs?
Compare your answer: The answer varies.
Explain why you think that graph does not belong.
Compare your answer: Your answer may vary, but here are some samples.
- A doesn't belong because: It is the only graph that has no maximum or minimum. It is the only situation in which the temperature does not change.
- B doesn't belong because: It is the only graph that has one maximum. It is the only graph that shows the temperature rising and then falling (but not rising again).
- C doesn't belong because: It is the only graph that has horizontal intercepts. It is the only graph that has one minimum. It is the only graph that shows negative output values or negative temperatures. It is the only graph that shows temperature falling and then rising (but not falling again).
- D doesn't belong because: It is the only graph that has several maxima and minima. It is the only graph where the temperature rises and falls several times. This graph shows a repeating pattern.
Why Should I Care?
Supratim Das is a PhD candidate at MIT who is interested in how batteries work and how to make them last longer. He believes that if we produce longer lasting batteries for our mobile devices and cars, we can reduce our overall energy consumption.
One of the most important mathemtical tools he has used is functions. Functions help him calculate the energy inputs and outputs and the changes that make a battery lose power.