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 only

II only

III only

I and III

II and III

### View Correct Answer

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.