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# Continuity of Functions Chapter Exam

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### Page 1

#### Question 1 1. Consider the function below. According to the intermediate value theorem, is there a solution to f(x) = 0 for a value of x between -5 and 5?

#### Question 2 2. What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?

#### Question 3 3. What are the regions of continuity given the following?

#### Question 4 4. What are the regions of continuity in this graph of f(x)?

#### Question 5 5. What are the regions of continuity in the graph of f(x) below?

### Page 2

#### Question 6 6. Consider the function f(x) below. Considering the intermediate value theorem and the vertical asymptote at x=0, is the following statement true or false? For any number C greater than 0, there is a positive value of x that satisfies the equation f(x)=C.

#### Question 7 7. What are the regions of continuity for y defined as?

####
Question 8
8.
Which of the following functions are discontinuous?

I) f(x) = x^2 + 1 when x < 0 and f(x) = x + 1 when x ≥ 0

II) f(x) = x when x < 0, f(x) = 1 when x = 0, and f(x) = -x when x > 0

III) f(x) = 2

#### Question 9 9. What type of discontinuity is in the graph of f(x) = {2 for x < 0; x+2 for x >= 0}?

#### Question 10 10. Which of the following functions is continuous for every value of x except x=0?

### Page 3

#### Question 11 11. Given the values of the continuous function f(x) below, how many solutions will there be to f(x)=4.1?

#### Question 12 12. I have a function where f(1) = 0 and f(4) = 3. Why might there not be an x between 1 and 4 such that f(x) = 1?

#### Question 13 13. Consider the equation below. Calculate f(0), f(1) and f(2). Given that information, how many solutions are there to f(x)=-1?

#### Question 14 14. What type of discontinuity is in the graph of f(x) = {x for x<-1; x+1 for x>=-1}?

#### Question 15 15. Given the function below, in what region will f(x) = 0?

### Page 4

#### Question 16 16. How many discontinuities are in the function f(x) = (1 - x)/[(3 - x)(2 - x)]?

####
Question 17
17.
Given y below and the intermediate value theorem, how many times will y = 0 between x = 0 and x = π?

(Hint: Work in radians since one of the parameters for x is π.)

#### Question 18 18. How many discontinuities are in this function?

#### Question 19 19. How many discontinuities are in the function f(x), where f(x) = -1 when x < -1, and f(x) = x for values of x ≥ -1?

#### Question 20 20. According to the intermediate value theorem, if you have a function where f(4) = 5 and f(6) = 3, there will be at least one point x between 4 and 6 where f(x) = 4.

### Page 5

#### Question 21 21. What type of discontinuity is in the graph of f(x) = 1/(x+2)?

####
Question 22
22.
Which of the following functions are continuous?

I) f(x) = 1/(x-1),

II) f(x) = abs(x)-x,

III) f(x) = x^2/2

#### Question 23 23. What type of discontinuity is in the graph of f(x) = {x for x<3; 0 for x=3; and x for x>3}?

#### Question 24 24. Which of the following continuous functions will have at least one solution to the following equation?

#### Question 25 25. Consider the function below. According to the intermediate value theorem, is there a solution to f(x) = 4 for a value of x between 4 and 7?

#### Continuity of Functions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!