# Continuity of Functions

### Quizzes

1. |
Which of the following statements is true? -> A bounded function on a closed interval [a,b] must be continuous. |

2. |
Let . For which interval can we use the Boundedness Theorem to conclude that f must be bounded on that interval? -> [1,2] |

3. |
Which of the following graphs shows a function that is both bounded and discontinuous on [a,b]? -> No. This function is not bounded on [ |

4. |
A continuous function on a closed interval [a,b] -> must be bounded on that interval but need not attain a maximum value on that interval. |

5. |
What is the maximum value of f(x) = sin(x) on the interval [π,2π)? -> 0 |

6. |
A continuous function on a closed interval [a,b] -> may attain its maximum and minimum value an infinite number of times each. |

7. |
Let . For which interval(s) can we use the Extreme Value Theorem to conclude that f must attain a maximum and minimum value on that interval? -> neither (a) nor (b) |

8. |
If f is continuous on [a,b] and f(b)<M<a) then the Intermediate Value Theorem tells us how many values of c exist in (a,b) with f(c) = M. |

9. |
Let the function . On which of the following intervals does the IVT guarantee the existence of a value c with f(c) = 0? -> (-3,0) |

10. |
Which of the following pictures best illustrates the IVT? -> Picture (d) |