# Continuity of Functions

### Quizzes

1. |
- Identify the picture(s) in which we can see what
*f*is doing for all values of*x*in the window.
I. II. |

2. |
Four different graphs of the function f(x) = 2x^{2} + 1 are shown below. Which picture best illustrates the fact that if x is within 0.06 of 2, then f(x) is within 0.5 of f(2) = 9? -> |

3. |
Which statement is true for the function f shown below? -> If |

4. |
We have a function f. We want f(x) to be within 0.5 of f(0). For which of the following functions do we have a guarantee that we can restrict x to find what we want? (x must be allowed to move the same distance from 0 in either direction, and x may not just be set equal to 0.) -> II and III |

5. |
If f(x) = 4 - 2x then when |x-1| < 0.5 we have a guarantee that |f(x)-2| < 1. Identify c, ε, and δ as commonly used in the definition of continuity. -> c = 1,ε = 1, δ = 0.5 |

6. |
Let f(x) = 3x + 1. Then f is continuous at 1 with f(1) = 4. Find the largest value of δ for which if x is within δ of 1, then f(x) is within 0.5 of 4. -> 0.16 |

7. |
Let Then f is continuous at 4 with f(4) = 2. Find the largest value of δ for which if x is within δ of 4, then f(x) is within 0.25 of f(4). -> 0.5 |

8. |
In the formal definition of continuity at x = c, -> ε describes how close we want f(x) and f(c), while δ describes how close x and c need to be. |

9. |
If the function f is continuous at c, then -> for every ε>0 we can find a δ>0 such that if |x-c| < δ then |f(x)-f(c)| < ε. |

10. |
- Let ,
*c*= 0, and ε = 0.1.
Which is the largest value of δ such that if | |