If and , which of the following statements are true about the graphs of and in the ?
|I.||The graphs are exactly the same.|
|II.||The graphs are the same except when .|
|III.||The graphs have an infinite number of points in common.|
Select an Answer
I and III
II and III
The correct answer is E.
Statement I is false: The function has the real line as its domain. The function has as its domain all values of except , because the value of the expression is undefined when is substituted for . This means that the graph of contains a point with -coordinate equal to ,but the graph of contains no such point.
Statement II is true: For any not equal to , the expressions and give the same value, since for , the expression . It follows that for , the graphs of and contain the same point with that .
Statement III is true: Since statement II is true, for every number not equal to , the point is on both the graph of and the graph of . Since there are infinitely many numbers not equal to , the graphs have an infinite number of points in common.