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Algebra Foundations

You will see how scientists track butterflies using graphs and functions.

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After completing this tutorial, you will be able to complete the following:

- Identify a graph with an increasing function.
- Identify a graph with a decreasing function.
- Identify a graph with a constant function.

When were the butterflies at a maximum distance from their starting point? How can you tell?

~ The butterflies were a maximum distance from their starting point at the beginning of month 5. We see that the graph has a maximum at the beginning of month 5, and this corresponds to the maximum distance from the butterflies' starting point.

Using the graph, how would you describe the motion of the butterflies between months 7 and 8?

~ Between months 7 and 8, the graph decreases at a nearly constant rate. This means that the butterflies flew some distance at a nearly constant rate toward their starting point.

When did the butterflies return to their starting point? How can you tell?

~ The butterflies return to their starting point at the beginning of month 10. We notice that the graph crosses the x-axis again at month 10, and this corresponds to the time at which the butterflies are a distance of 0 kilometers from their starting point.

Can you think of any other situations or examples that may be modeled by the graph given above?

~ Answers will vary. If we change the units on the vertical and horizontal axis and focus only on the shape of the graph, then we have many options. For instance, the graph may model a person's distance from home as they run errands on a weekend afternoon.

Approximate Time | 2 Minutes |

Pre-requisite Concepts | Students should be able to define the following terms: constant slope, horizontal line, concave up, maximum value, and increasing and decreasing parts of graphs. |

Course | Algebra Foundations |

Type of Tutorial | Animation |

Key Vocabulary | concave up, constant slope, decreasing |