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Question : Find all values x = a where the function is discontinuous. 10) f(x) = (-9x/(7x - 5)(-8 - 8x)) : 2151559

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find all points where the function is discontinuous.

1)

A) x = 4

B) x = 2

C) None

D) x = 4, x = 2

2)

A) x = 1

B) None

C) x = -2

D) x = -2, x = 1

3)

A) x = 2

B) x = -2, x = 0, x = 2

C) x = -2, x = 0

D) x = 0, x = 2

4)

A) x = 6

B) x = -2

C) None

D) x = -2, x = 6

5)

A) None

B) x = 4

C) x = 1, x = 4, x = 5

D) x = 1, x = 5

6)

A) None

B) x = 0

C) x = 0, x = 1

D) x = 1

7)

A) x = 0, x = 3

B) x = 3

C) x = 0

D) None

8)

A) x = -2, x = 2

B) None

C) x = 2

D) x = -2

9)

A) x = -2, x = 0, x = 2

B) x = -2, x = 2

C) x = 0

D) None

Find all values x = a where the function is discontinuous.

10) f(x) = (-9x/(7x - 5)(-8 - 8x))

A) Nowhere

B) a = (5/7), 1

C) a = (5/7), - 1

D) a = 0, (5/7), - 1

11) f(x) = (|x^{2} - 4|/x - 4)

A) Nowhere

B) a = -2, 2, 4

C) a = 4

D) a = 2, 4

12) f(x) = (x^{2} - 9/x + 3)

A) a = -9

B) a = 3

C) a = 2

D) a = -3

13) g(x) = {(0if x< 0)

(x^{2} - 5xif 0 ≤ x ≤ 5)

(5if x > 5)

A) a = 5

B) Nowhere

C) a = 0, 5

D) a = 0

14) q(x) = x^{2} + 5x - 8

A) a = 8

B) a = 0

C) Nowhere

D) a = 5

15) k(x) = e^{√(x + 7)}

A) a < -7

B) a > -7

C) a > 7

D) Nowhere

16) f(x) = ln|(x - 5/x + 2)|

A) a = -2

B) a = 5, -2

C) a = -5, 2

D) Nowhere

17) f(x) = {(5 if x < 3)

(x + 6 if 3 ≤ x ≤ 9)

(15 if x > 9)

A) a = -3

B) Nowhere

C) a = 3

D) a = 9

18) f(x) = {(5 if x < 4)

(x^{2} - 11 if 4 ≤ x ≤ 8)

(5 if x > 8)

A) a = 8

B) a = 4

C) a = 11

D) Nowhere

19) f(x) = {(4x - 6 if x < 0)

(x^{2} + 3x - 6 if x ≥ 0)

A) a = 3

B) a = -6

C) a = 0

D) Nowhere

Give an appropriate response.

20) Find the limit of f(x) as x approaches 3 from the right.

f(x) = {(-2if x < 3)

(x + 2if 3 ≤ x ≤ 5)

(7if x > 5)

A) 5

B) 7

C) -2

D) The limit does not exist.

21) Find the limit of f(x) as x approaches 3 from the left.

f(x) = {(-2if x < 3)

(x + 2if 3 ≤ x ≤ 5)

(7if x > 5)

A) 7

B) 5

C) -2

D) The limit does not exist.

Find the value of the constant k that makes the function continuous.

22) h(x) = {(x^{2} if x ≤ 3)

(x + k if x > 3)

A) k = 12

B) k = 3

C) k = 6

D) k = -3

23) g(x) = {(x^{2} - 7 if x < 6)

(5kx if x ≥ 6)

A) k = (6/5)

B) k = (29/30)

C) k = 13

D) k = 29

24) f(x) = {(x^{2} + x + k if x < -2)

(x^{3} if x ≥ -2)

A) k = -6

B) k = 2

C) k = -8

D) k = -10

25) h(x) = {((7x^{2} + 10x - 8/x + 2) if x ≠ -2)

(4x + k if x = -2)

A) k = -10

B) k = 30

C) k = 0

D) k = 2

Use a graphing utility to find the discontinuities of the given rational function.

26) f(x) = (x^{2} + 2x + 1/x^{3} + 2x^{2} + 9x - 12)

A) -1

B) 1

C) 3

D) The function is continuous for all values of x.

27) f(x) = (x + 1/x^{3} + 2x^{2} + 6x - 9)

A) 3

B) 1

C) -1

D) The function is continuous for all values of x.

Solve the problem.

28) The graph below shows the amount of income tax that a single person must pay on his or her income when claiming the standard deduction. Identify the income levels where discontinuities occur and explain the meaning of the discontinuities.

Income Tax, 1000's of dollars

Income, 1000's of dollars

A) Discontinuities at x = $22,000, x = $44,000, and x = $60,000. Discontinuities represent tax cheating on the part of high-income earners.

B) Discontinuities at x = $22,000, x = $44,000, and x = $60,000. Discontinuities represent boundaries between tax brackets.

C) Discontinuities at x = $44,000 and x = $60,000. Discontinuities represent tax shelters.

D) Discontinuities at x = $44,000 and x = $60,000. Discontinuities represent boundaries between tax brackets.

29) In order to boost business, a ski resort in Vermont is offering rooms for $125 per night with every fourth night free. Let C(x) represent the total cost of renting a room for x days. Sketch a graph of C(x) on the interval (0, 6] and determine the cost for staying 4(1/2) days.

A) C(4(1/2)) = $500

B) C(4(1/2)) = $625

C) C(4(1/2)) = $375

D) C(4(1/2)) = $500

30) Suppose that the cost, p, of shipping a 3-pound parcel depends on the distance shipped, x, according to the function p(x) depicted in the graph. Is p continuous at x = 50? at x = 500? at x = 1500? at x = 3000?

A) No; no; yes; no

B) Yes; no; yes; no

C) Yes; yes; yes; no

D) Yes; no; no; no

31) Suppose that the cost, C, of producing x units of a product can be illustrated by the given graph. Is C(x) continuous at x = 50? x = 100? x = 150?

A) No; no; no

B) Yes; yes; yes

C) Yes; no; no

D) Yes; no; yes

32) Suppose that the unit price, p, for x units of a product can be illustrated by the given graph. Is p(x) continuous at x = 50? x = 100? x = 150?

A) Yes; no; yes

B) No; yes; yes

C) No; yes; no

D) No; no; no

33) Consider the learning curve defined in the graph. Depicted is the accuracy, p, expressed as a percentage, in performing a series of short tasks versus the accumulated amount of time spent practicing the tasks, t. Is p(t) continuous at t = 25? at t = 40? at t = 45?

A) Yes; no; yes

B) Yes; no; no

C) Yes; yes; yes

D) No; no; no