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# Continuity in AP Calculus: Help and Review Chapter Exam

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 "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!

### Page 1

#### Question 1 1. 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 2 2. Given the function below, in what region will f(x) = 0?

#### Question 3 3. What type of discontinuity is in the graph of f(x) = {2 for x < 0; (x + 2) for x ≥ 0}?

#### Question 4 4. Which of the following functions is continuous for every value of x except x=0?

#### Question 5 5. What are the regions of continuity for y defined as?

### Page 2

#### Question 6 6. 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 7 7. What type of discontinuity is in the graph of f(x) = 1/(x+2)?

#### Question 8 8. 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 9 9. How many discontinuities are in the function f(x) = (1 - x)/[(3 - x)(2 - x)]?

#### Question 10 10. What are the regions of continuity given the following?

### Page 3

#### Question 11 11. 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 12 12. What are the regions of continuity in this graph of f(x)?

#### Question 13 13. What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?

#### Question 14 14. 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?

#### Question 15 15. Which of the following continuous functions will have at least one solution to the following equation?

### Page 4

#### Question 16 16. 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 17 17. Given the values of the continuous function f(x) below, how many solutions will there be to f(x)=4.1?

####
Question 18
18.
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 19 19. What type of discontinuity is in the graph of f(x) = {x for x < -1; (x + 1) for x ≥ -1}?

#### Question 20 20. What type of discontinuity is in the graph of f(x) = {x for x < 3; 0 for x = 3; and x for x > 3}?

### Page 5

####
Question 21
21.
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 22 22. 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.

#### Question 23 23. How many discontinuities are in this function?

#### Question 24 24. What are the regions of continuity in the graph of f(x) below?

####
Question 25
25.
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.)

#### Continuity in AP Calculus: Help and Review 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 "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!