Lesson 4
1. Lesson 4
1.11. Explore 7
Module 7: Absolute Value and Reciprocal Functions
If you were asked to identify the reciprocal of the number 2, you would say 
. What if you were asked to identify the reciprocal of ? The answer, of course, is 2. This shows that the reciprocal of a reciprocal is the original number!
Consider a question phrased this way:
“If the reciprocal of a number is 
, then what is the number?”
This question is really asking for the reciprocal of .
You can adopt a similar approach in graphing functions when given the graphs of reciprocal functions. For example, consider the question:
“If the graph of 
is shown, then what does the graph of y = f(x) look like?”
For this question, you can simply graph the reciprocal function using any of the strategies that you have previously learned. After all, the reciprocal of 
is y = f(x) and vice versa. In fact, the question might as well be stated as:
“If the graph of y = f(x) is shown, then what does the graph of 
look like?”
Turn to “Example 4” on page 401 to work through an example similar to what has been described above. You have to sketch the original function when given a graph of its reciprocal. Look carefully for the answers to the following questions.
- What property of the graph of a function corresponds to a vertical asymptote?
- How does the location of a vertical asymptote on the graph of a reciprocal function help you to determine the equation of the original function?
Self-Check 4
Turn to pages 403–406 of your textbook to practise applying the concepts that you have learned. Complete questions 2.b. and d., 9, and 10. Check the solutions in the back of the textbook to make sure you are doing the questions correctly. You may also want to review relevant parts of the lesson as you work through the questions.