# A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at

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Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x a and is continuous at a. (If the discontinuity is not removable, enter NONE.) 1. f(x)= (x^4-1)/(x-1), a=1

2. ## Calculus

Hi! My question is: Given that f is a function defined by f(x) = (2x - 2) / (x^2 +x - 2) a) For what values of x is f(x) discontinuous? b) At each point of discontinuity found in part a, determine whether f(x) has a limit and, if so give the value of the

3. ## Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

4. ## Calculus

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. Okay, I presume that the [] brackets denote the greatest integer function (int ()

5. ## precalculus

The function has a vertical asymptote of x=2 The function has a removable discontinuity of x=-2 The function has a horizontal asymptote of y= 0 No x intercept Y-intercept is (0,-0.5) End Behavior f(x) --> 0, x? -oo f(x) ? 0, x ? oo What is the rational

6. ## Algebra 2 H

Find x-values if any at which the function f(x)=13x^2-15x-15 is not continuous. Which of the discontinuities are removable? THANKS YOU!!

7. ## calculus

give an example of a function that has: a) only one point of discontinuity b) exactly two ponts of discontinuity c) an infinite number of discontinuity give an example of a function that is: a) continuous at every point b) discontinous at every point i am

8. ## math

How do I find the continuity or discontinuity of a graphed function? I am stuck on this problem and cannot whatsoever get past it.

9. ## Calculus

Given f(x) = (x^4 + 17) / (6x^2 + x - 1) Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. From the work that I have done so far, I know that there are two

10. ## math

Use a graph to determine whether the given function is continuous on its domain. HINT [See Example 1.] f(x) = x + 7 if x < 0 2x − 5 if x ≥ 0 1 continuous discontinuous If it is not continuous on its domain, list the points of discontinuity. (If there

11. ## calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)= x2+10x+26 2 −x2−10x−24 if

12. ## Calculus (Any Help At All Is Really Appreciated)

Suppose g(x) = { 1 / (x-2) if x < 1 2x - 3 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontuity C.) has an infinite discontuity D.) has a removable discontuity E.) None of the

13. ## ap calculus

Find the discontinuities of f(x)= ((x^2)+5x+6)/((x^2)-4)and categorize them as removable or non removable.

14. ## Calculus

Suppose g(x) = { 1 / (x - 2) if x < 1 2x - 4 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontinuity C.) has an infinite discontinuity D.) has a removable discontinuity E.) None

15. ## Math (Continuity)

Find the x-values (if any) at which f is not continuous. Which of the discontinuties are removable? f(x)=(x)/(x^2-4) I'm not sure how to do this problem but I know that it is not continnous at x=2?

16. ## Calculus

Let f(x)=(2x^2+5x-7)/(x-1) show that F(x) has a removable discontinuity at x=1 and determine what value for F(1) would make f(x) continuous at x=1 I'm not sure how to factor to solve for f(1)..

17. ## clalc

Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0. how would you do this if you were given two graphs: discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola) then discontinuity at

18. ## Algebra 2

Find any points of discontinuity for the rational function. 1. (x + 6)(x + 2)(x + 8) y = _____________________ (x + 9)(x + 7) 2. x - 8 y = _____________________ x^2 + 6x - 7

19. ## Pre Cal

which of the following best describes the behavior of thre function f(x)=(x^2-2x)/(x^2-4) at the values not in its domain? a) one vertical asymptote, no removable discontinuities b) 2 vertical asymptotes c) two removable discontinuities d) one removable

20. ## Math

Describe the intervals on which the following function is continuous. If not continuous, state "where" the discontinuity occurs and state the TYPE of discontinuity. f(x)= (x^2-x-12)/(x^2-6x+8) I just don't understand how to find the intervals. Thanks~

21. ## Calculus - Discontinuity

What kind of discontinuity is this piecewise function? Removable or jump? f(x) ={ (2x^2 - 5x - 3)/(x-3) if x does not equal 3 ............6............................if x = 3

22. ## Chemistry-inorganic

Explain the discontinuity in the trend for the first ionization energies between Mg and Al, also P and S.

23. ## Calculus

Which of the following must be true for the graph of the function f(x)= (x^2-25)/5x-25) There is: I. a removable discontinuity at x=5 II. a vertical asymptote at x=5 III. an infinite discontinuity at x=5 possibles answers: a) I only b) II only c) III only

24. ## Calculus

Could anyone please help me figure out the discontinuity that is removable of the following function?? Any help would be greatly appreciated! Thanks in advance!!! f(x)=4x/x^2+x-2

25. ## math calculus

what does this function show at x=5? f(x)=^2-25/x-5 A. removable discountinuity B. jump discountinuity C. infinite discountinuity D. Countinuity E. None of the above

26. ## Calculus

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. Okay, I presume that the [] brackets denote the greatest integer function (int ()

27. ## Algebra 2

What are the points of discontinuity? Are they all removable? Please show your work. ￼￼￼ y=(x-5) / x^2 - 6x +5

28. ## Math - PreCalc (12th Grade)

What does this function show at x = 5? f(x)=x^2−25/x−5 A) removable discontinuity B) jump discontinuity C) infinite discontinuity D) continuity E) none of the above

29. ## Pre-Calc/Trig

Identify the asymptotes, removable discontinuities, and intercepts for the graph of the function. d(x)=(x^2-12x+20)/3x

30. ## Math - PreCalc (12th Grade)

What value must be defined for f(4) to remove the discontinuity of this function at x=4? f(x)=(x^2−16)/(x−4) A) 0 B) 4 C) -4 D) 8 E) -8 f(4)=(4^2−16)/(4−4) f(4)=0/0 you can't divide by zero. I don't understand the question.

31. ## calculus

Let f(x) = [(2x2+4 x −70)/(x−5)] Show that f(x) has a removable discontinuity at x=5 and determine what value for f(5) would make f(x) continuous at x=5 Must define f(5)= I've been stuck on this problem for some time how would i do this one? Ty!

32. ## AP CALC. AB

1.Locate the discontinuity of the function y=1/(1+sin x) 2.Suppose that f is a continuous function defined for all real numbers x and f(-5)=3 and f(-1)=-2 . If f(x) = 0 for one and only one value of x, then which of the following could be x?

33. ## calculus

Find the discontinuities of the given function. Classify them as a point discontinuity or a jump discontunuity. g(x)= x, x= -3

34. ## calculus

Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0. how would you do this if you were given two graphs: discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola) then discontinuity at

35. ## calculus

find the x-values at which f is not continuous. which of the discontinuities are removable? f(x)=1/(x^2+1)

36. ## Calculus - #2

Suppose g(x)={x^2+2x+1/x+1 if x

37. ## Calculus - #1

Suppose g(x)={1/x+1 if x

38. ## Pre Calculus

Determine all discontinuities that exist on the graph of y = f(x) shown below. Please show your reasoning by justifying your answer with the conditions of continuity. If there is a discontinuity, identify it as removable or non-removable.

39. ## Pre-Calculus

(I NEED URGENT HELP FOR THIS) Given the info. that a rational function has a vertical asymptote of x=3 and x=-3, horizontal asymptote at y=-4, no x-intercepts, and y-intercept: (0,2/3), no removable discontinuity, and no end behavior, what would the

40. ## Precalc

Find an equation of a rational function that satisfies the given conditions. Vertical asymptote: x = 4 Horizontal asymptote: y = 0 X-intercepts: none Y-intercepts (0, -1/4) Multiplicity of 1 Removable discontinuity: x = 1 End behavior: x --> infinity, f(x)

41. ## Calculus

Let f(x)=|x+1|/(x^(2)-1). Is f continuous? If not,classify any points of discontinuity as infinite, jump, or removable. Sketch the graph of y=f(x) for -4

42. ## Calculus

Suppose g(x) = { 1 / (x-2) if x < 1 2x - 3 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontuity C.) has an infinite discontuity D.) has a removable discontuity E.) None of the

43. ## Calculus AB

Suppose g(x) = { 1 / (x-2) if x < 1 {2x - 3 if x >/= 1 The best description concerning the continuity of g(x) is that the function A.) is continuous B.) has a jump discontuity C.) has an infinite discontuity D.) has a removable discontuity E.) None of the

44. ## asymptotes and discontinuity 2???

consider the function f(x) = 1/x - 1 for x not=0 and f(x) = 0 for x = 0. decide whether f(x) has a)one symptote and two discontinuities b)two asymptotes and two discontinuities c)two asymptotes and one discontinuity I'm not sure if you mean 1/(x-1) or

45. ## Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)=2x^2+3x–14/x–2 Show that f(x)

46. ## Calculus (Discontinuity)

Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite, or jump discontinuities. Okay, I presume that the [ ] brackets denote the greatest integer function (int () ). Once I

47. ## precalcus

what is the rational equation of a function with intercepts at (8,0) and (0,0.16) and a horizontal asymptote at y=0.5 and a vertical asymptote at x=3 and a removable discontinuity at (3,-1)

48. ## algebra

Find the points of discontinuity and any holes. y=x^2-1/(x^2+3x+2) please and thank you y =(x^2-1)/((x+1)(x+2)) =(x-1)/(x+2) we cancelled the (x+1)/(x+1) which is 0/0 for x=-1 so in our simplified expression when x=-1 y = -2 There is a "hole" at (-1,-2) in

49. ## pre calc

The Identity Function The Squaring Function The Cubing Function The Reciprocal Function The Square Root Function The Exponential Functional Lo The Natural Logarithum Function The Sine Function The Cosine Function The Absolute Value Function The Greatest

50. ## Math

How do I know if a graph has removable continuity, jump, or infinite? What is the difference?

51. ## calculus

identify and explain all the kinds of discontinuity for y = (x + 4)/(x^2 - 16)

52. ## Algebra

The Graph of F(x) = (x^2 -2x -8)/(x+6) has which of the following ? a) point of discontinuity b) vertical asymptote c) both of the above d) neither of the above i guess a) not sure, can someone help me

53. ## Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

54. ## Calculus

What kind of discontinuity is this: F(x)= (2x^2 - 5x -3)/(x-3) if x does not equal 3 6 if x=3 It is a pieces use function. I thought it was removable but my answer key says it is a jump discontinuity. This is from an exam review and I want to get it right.

55. ## AP Calculus

Are infinite discontinuities removable? Also, please help me with this question: f(x)=x^2+4x+3 / x^2-9 has one removable discontinuity and one vertical asymptote. Find and identify the x-value for each. I found the asymptote at x=3, but please help for the

56. ## calculus

Hi, I am lost on couple of problems and i was wondering if you could just help me out with them. 1. Find and classify the points of discontinuity of the function F(x) = (x^2+7x+12)/(x^3-9x) now for this problem i know there is going to be an infinite

57. ## Math

I've got quite a few problems. Please answer any of them in whole or in part. Thank you in advance. (For the record, you're not doing my homework; you're helping me understand it. These problems were not assigned.) (1). Determine the discontinuities and

58. ## Pre-Calc

I really need to understand wha tmakes a graph have these discontinuities 1)Removable 2)Non-Removable and how to tell them in a function

59. ## Calculus

suppose f(x) = {x-1/x^4-1 if x

60. ## math

Can someone please help me with these few problems here? Find the holes and points of discontinuity: 12x^4+10x-3 ----------- x-1 and 12x+24 ------ x^2+2x In the first, examine x=1 and in the second, examine x=-2. Look at the numerator also at that same

61. ## infinite discontinuity

How do check the graph of a function has an infinite discontinuity at a point or not? (without the help of a graphing calculator) example: Check whether y = (x^2-9)/(3x-9) has an infinite discontinuity at x = 3 or not CAn you get rid of the denominator?

62. ## Calculus AB

Please help I'm stuck on this problem for the past hour. Define f(x)= { Ln lx-1l }/x A) show that f(c) is continuous at x=2 B)Where on the interval [-2,2] is f discontinuous? Show the work that leads to your conclusion. C) classify the discontinuities in

63. ## Calculus

Find all points of discontinuity f(x) = [x^2 + 5x - 2]/ [x^2 - 9]

64. ## Calculus - #3

Suppose g(x)={1/(x-2) if x

65. ## Calculus - #4

Suppose g(x)={1/(x-2) if x

66. ## Calculus (Discontinuities)

Suppose, f(x) = { (x - 1)^2 / x + 1 if x < 2 (x^2 - 2x - 8)/(x - 4) if 2

67. ## Math

I need to give an example of a function with at least one removable and one non-removable discontinuity. I am not to sure how to do this. Please explain! Thanky you

68. ## Calculus

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x)=2x^2+3x–14/x–2 Show that f(x)

69. ## Calculus

Suppose f(x) = (x-1)^2/x+1 if x < 2 (x^2-2x-8)/x-4 if 2

70. ## CALCULUS

i needed help on some problems and clarification on one. 1. Determine the location and type (removable, jump, infinite, or other) of all discontinuities of the function (x^2-3x+2)/(x^2-1) this section has been confusing for me for some reason, can any one

A function g(x) has the following characteristics: 1) It is rational with a quadratic polynomial in both the numerator and the denominator. 2) It has a removable discontinuity at x=1 and the limg(x) as x approaches 1 is -1/9 3) The graph of g(x) has a

72. ## AP Calculus

A function g(x) has the following characteristics: 1) It is rational with a quadratic polynomial in both the numerator and the denominator. 2) It has a removable discontinuity at x=1 and the limg(x) as x approaches 1 is -1/9 3) The graph of g(x) has a

73. ## Calculus

x(squared)+8x+17 if x < or = -4 Let f(x)= 2 if x= -4 -x(squared)-8x-15 if x > -4 Show that f(x) has a removable discontinuity at x=–4 and determine what value for f(–4) would make f(x) continuous at x=–4. Must redefine f(–4)=____

74. ## calculus

Find the points of discontinuity on [-3,5] for the function f(x)=[[x-1]], where the double bracket indicates the greatest integer function.

75. ## Math

What are the points of discontinuity (if any) in the following function? y=(2x-1)^(1/3) Thanks

76. ## calculus

find the points of discontinuity of the given function f(x) =x+3/|x2+3x|

77. ## math calculus

What value must be defined for f(4) to remove the discontinuity of this function at x = 4? f(x)= x^2-16/x-4 0 4 -4 8 -8

78. ## Calculus

What type of discontinuity is this? f(x) = 2x+8,x4 I think it's a point discontinuity.

79. ## Algebra

Find any points for the discontinuity for the rational function. I think the answer is D. y=(x-8)/(x^2+5x-6) A. x=8 B. x= -1, x= 6 C. x= 1, x=6 D. x=1, x= -6

80. ## calculus

Continuous/discontinuity Can someone please tell me how to make this determination? 1/x(x-3) x=0,x=-4 is the function con @ x=3 is the function con @ x=0 is the function con @ x=-4

81. ## Pre-Calculus

sketch f(x) such that f(x) is increasing on (-inf,-2) and f is decreasing on (-2,0), f(x) has point discontinuity at x=-2, f(x) has a horizontal asymptote of y=4, f(x) is an odd function.

82. ## Math/Algebra

Sketch the graph of each piecwise-defined function. Determine the domain and range. Identify each point of discontinuity. f(x)= -x if x

83. ## Calculus

I am having trouble with this question and I am unsure how to solve it... True or False (with justification) The function sin(x) if x ≤ 0 f(x) = 1+cos(x) if x>0 has a jump discontinuity at x = 0.

84. ## Math

(1) State the conditions for a singled-valued function of x to be continuous at x = a (2) find the points of discontinuity of the functions (i) x^3 + 4x + 6 / x^2 - 6x + 8 (ii) sec x (3) Differentiate from the first princiaples (i) x^3 + 2x - 1

85. ## Math

Create a function which has the following properties: a. It has a horizontal asymptote at y=2 b. It has a discontinuity at x=2 which is not a vertical asymptote c. It has no other discontinuities or asymptotes

86. ## Algebra

Use the function below to answer the following parts. f(x) = 1/3x - 4 if -6 ¡Ü x < ¨C 3 2 if ¨C 3 < x < 3 x^2 ¨C 4 if x > 3 I know that: Domain= [-6,infinity] Range= [-6,infinity] and points of discontinuity = x=-3,x=3 How do i graph these functions?

87. ## calc

The derivative of a function f is f'(x) = x^2 - 8/x: Then at x = 2, f has A. an infection point B. a relative maximum C. a vertical tangent D. a discontinuity E. a relative minimum how do you test for all of these?

88. ## Computers

1.State the name of the removable disk which was invented in 1962. 2.Who invented the removable disk?

1.State the name of the removable disk which was invented in 1962. 2.Who invented the removable disk?

90. ## Calculus

Create a function which has the following properties: a. It has a horizontal asymptote at y=2 b. It has a discontinuity at x=2 which is not a vertical asymptote c. It has no other discontinuities or asymptotes Explain how your answer satisfies the previous

91. ## math calculus

For the function: f(x)= 2+x-x^2/ (x-1)^2 ; f'(x)= x-5/(x-1)^3 ; f''(x)=2x-14/(x-1)^4 a)find vertical and horizontal asymptotes. Examine vertical asymptote on either side of discontinuity. b)find any local extrema c)find points of inflection

92. ## Algebra

Use the function below to answer the following parts. 1/3x - 4 if -6 3 I found out the domain, range, and points of disontinuity. I think i did them right: Domain= [-6,infinity] Range= [-6,infinity] and points of discontinuity = x=-3,x=3 How do i graph

93. ## Calculus

Find the points of discontinuity. f(x) = { 16/x^2 if x ≥ 2 { 3x - 2 if x < 2

94. ## Calculus

In the exercise below find the x-values at which f is not continuous. Which of the discontinuities are removable? f(x) = csc2x

95. ## 12th Calculus

1. Explain why the function f(x)=(x^2-4)/(x-2) is not continous on [0,3]. what kind of discontinuity occurs? 2. use areas to show that integral sign with the upper limit of 3 and a lower limit of 0 (x^2-4/x-2)dx=10.5 3. use the area to show that intergral

96. ## calculus

evaluate the improper interval with an interior discontinuity dx/x^3 from -1 to 2

97. ## MATH

What are the vertical asymptotes and the point of discontinuity for: x^3-2x^2+x/x^3-x^2-2x Does it intersect any asymptote?

98. ## Calculus

I need some help on getting ideas for my limits & continuity calculus project! For the limits project: I have to conduct an "interview with a limit" (Q&A format).I have to include factual information like definitions, properties, theorems, etc. I also have

99. ## Math- Ideas only

I need some help on getting ideas for my limits & continuity calculus project! For the limits project: I have to conduct an "interview with a limit" (Q&A format).I have to include factual information like definitions, properties, theorems, etc. I also have

100. ## earth science

The Mororovicic Discontinuity marks the change in rock density and elasticity between the: