# NMTA Essential Academic Skills Math: Continuity Chapter Exam

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

#### Question 2 2. Which of the following answer possibilities describes a function that the intermediate value theory applies to?

#### Question 3 3. 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 4 4. If all we know about the following functions is that they're continuous, and the given values, then which will have a solution for f(x) = 2?

#### Question 5 5. Given y below and the intermediate value theorem, how many times will y = 0 between x = 0 and x = π?

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

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

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Question 10
10.
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

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#### Question 11 11. 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 12 12. What type of discontinuity is in the graph of f(x) = {2 for x < 0; x+2 for x >= 0}?

#### Question 13 13. 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 14 14. What type of discontinuity is in the graph of f(x) = 1/(x+2)?

#### Question 15 15. What type of discontinuity is in the graph of f(x) = {x for x<-1; x+1 for x>=-1}?

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#### Question 16 16. What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?

#### Question 17 17. What are the regions of continuity in this graph of f(x)?

#### Question 18 18. What are the regions of continuity in the graph of f(x) below?

#### Question 19 19. What are the regions of continuity given the following?

#### Question 20 20. What are the regions of continuity for y defined as?

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#### Question 21 21. Which of the following functions is continuous for every value of x except x=0?

#### NMTA Essential Academic Skills Math: Continuity 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!