Continuity in AP Calculus: Homework Help Resource Chapter Exam

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!

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Question 1 1. 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 2 2. 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 3 3. Which of the following continuous functions will have at least one solution to the following equation?

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

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

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Question 6 6. How many discontinuities are in the function f(x), where f(x) = -1 when x is less than -1, and f(x) = x for values of x>=-1?

Question 7 7. What are the regions of continuity given the following?

Question 8 8. 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 9 9. How many discontinuities are in this function?

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

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Question 11 11. What are the regions of continuity for y defined as?

Question 12 12.

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

Question 14 14. 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 15 15. What type of discontinuity is in the graph of f(x) = 1/(x+2)?

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Question 16 16.

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 17 17. 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 18 18. 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 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. Given the function below, in what region will f(x) = 0?

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Question 21 21. What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?

Question 22 22. Given the values of the continuous function f(x) below, how many solutions will there be to f(x)=4.1?

Question 23 23. How many discontinuities are in the function f(x) = (1 - x)/[(3 - x)(2 - x)]?

Question 24 24. 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 25 25. Given y below and the intermediate value theorem, how many times will y = 0 between x = 0 and x = π?

Continuity in AP Calculus: Homework Help Resource 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!

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