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Analyzing and Comparing the Properties of Graphs

4.9.1 Analyzing and Comparing the Properties of Graphs

4.9.1 • Analyzing and Comparing the Properties of Graphs

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.

A line graph with time on the x-axis and temperature on the y-axis. A red horizontal line shows temperature remains constant over time.

Graph A

 A graph with temperature on the y-axis and time on the x-axis, showing a red curve that rises, peaks in the middle, then falls, illustrating temperature change over time.

Graph B
A graph with temperature on the y-axis and time on the x-axis shows a red curve forming a U-shape, indicating temperature decreases then increases over time.

Graph C

 A line graph showing temperature on the y-axis and time on the x-axis, with a red wave-like curve indicating temperature fluctuating up and down over time.

Graph D
Graphs A-D illustrate diverse temperature changes over time, including constant, increasing/decreasing, and fluctuating patterns.
1.

Which graph do you think does not belong in a group with the other 3 graphs?

Compare your answer: The answer varies.

2.

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?

A person charges an orange electric car at a charging station with a solar panel, wind turbines, and hills in the background, representing clean energy and sustainability.

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.