TExES Physics/Math 7-12: Continuity in Calculus 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. What are the regions of continuity for y defined as?

Question 2 2. 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 3 3. Given the function below, in what region will f(x) = 0?

Question 4 4. Which of the following continuous functions will have at least one solution to the following equation?

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

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Question 6 6. Given the values of the continuous function f(x) below, how many solutions will there be to f(x)=4.1?

Question 7 7. 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 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. 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 10 10. What are the regions of continuity in this graph of f(x)?

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Question 11 11. Which of the following functions is continuous for every value of x except x=0?

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

Question 14 14. What type of discontinuity is in the graph of f(x) = x/((x+1)(x-3))?

Question 15 15. 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?

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

Question 17 17. What type of discontinuity is in the graph of f(x) = {x for x<-1; x+1 for x>=-1}?

Question 18 18. How many discontinuities are in the function f(x) = (1 - x)/[(3 - x)(2 - x)]?

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

Question 20 20.

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

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

TExES Physics/Math 7-12: Continuity in Calculus 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!

TExES Physics/Mathematics 7-12 (243): Practice & Study Guide  /  Math Courses
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