Lesson 4

Lesson 4 Summary

 

In this lesson you investigated the following questions:

• How are the properties of reciprocals related to the properties of reciprocal functions?

• What are the strategies for graphing the reciprocal of a function?

In this lesson you learned that the graph of the reciprocal of a function can be obtained by plotting the point  for every point (x, y) on the original function. Since it would not be efficient to transform each point on the function, you explored other graphing strategies. One strategy was to use a table to track a set of points.

 

Another strategy for graphing reciprocal functions that you learned is based on the properties of reciprocals. The A.I.M. method quickly allows you to identify key properties of the graph, including locations of asymptotes, y-intercepts, and the direction of each part of the curve.

 

Throughout this lesson, you saw how the properties of reciprocals are applied in the graphing of reciprocal functions. You saw how the

• undefined reciprocal of zero translates into a vertical asymptote
  
  
• fact that the reciprocal of 1 is also 1, and the reciprocal of –1 is also –1, translates into invariant points
  
  
• contrary motion of a set of numbers and their reciprocals translates into the opposing directions of functions and their reciprocals

You will continue to study different types of functions in the future. Your understanding of the properties of these functions will help you to use them to model real-world situations.