# A continuous function f has domain of all real numbers. If f(-1) = 5 and f(1) = -5, explain why function f must have at least one zero in the interval [-1, 1]

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1. ## Algebra plz help

1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/ Range:O/ 2.Determain whether

2. ## Algebra

1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8}**** B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/ Range:O/ 2.Determain whether

3. ## Pre-Calculus

A rectangle is bounded by the x-axis and the semicircle y = √36 – x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers except x = 36 all real numbers

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is even. The function f has an

5. ## alebra

Let f(x)=2x^2+x-3 and g(x)=x-1. Perform the indicated operation then find the domain. (f*g)(x) a.2x^3-x^2-4x+3; domain:all real numbers b.2x^3+x^2-3x; domain: all real numbers c.2x^3+x^2+4x-3; domain: negative real numbers d.2x^3+x-3x+3; domain: positive

6. ## Math

The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. Find g ′(0) and g ″(0) in

7. ## Calculus

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true? I. g(x) = 1 at least once II. lim g(x) = g(3.5) as x aproaches 3.5. III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches

8. ## MATH HELP

A school puts on a play. The play costs \$1,200 in expenses. The students charge \$4.00 for tickets. There will be one performance of the play in an auditorium that seats 500 people. What is the domain of the function that shows the profit as a function of

9. ## Calculus

If f(x) is a continuous function defined for all real numbers, f(-1)=1, f(-5)=-10, and f(x)=0 for one and only one value of x, then which of the following could be that x value? a) -6 b) -5 c) -4 d) 0

10. ## Algebra 2

A function is created to represent the amount of money in your checking account. What restrictions would be made to the domain? -The domain would include all real numbers.* -The domain would only include positive integers. -The domain would only include

11. ## Algebra 2

A function is created to represent the costs of living per person in the family. What restrictions would be made to the domain? A-domain includes positive integers B- domain includes positive numbers C-domain includes all real numbers D- domain includes

12. ## Algebra 2

3. Identify the vertex and the axis of symmetry of the graph of the function y = 3(x + 2)2 – 3. (1 point) A- vertex: (2, –3); axis of symmetry: x = 2 B- vertex: (–2, –3); axis of symmetry: x = –2 C- vertex: (2, 3); axis of symmetry: x = 2 D-

13. ## 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

14. ## algebra

Can someone check my answers please and if Im wrong please explain. 1) graph 4x^2+4y^2=64. what are the domain and range? domain;all real numbers range;-4

15. ## math

Solve for the constants a and b that make the piecewise function continuous for all real numbers. f(x)= 4-2x-x^2, x1

Please check urgently .I have to submit the assignment A give an example of a function whose domain equals the set of real numbers and whose range equals the set? the set {-1,0,1} BGive an example of a function whose domain equals (0,1)and whose range

17. ## Calculus

Explain, using the theorems, why the function is continuous at every number in its domain. F(x)= 2x^2-x-3 / x^2 +9 A) F(x) is a polynomial, so it is continuous at every number in its domain. B) F(x) is a rational function, so it is continuous at every

18. ## Calculus

If f(x) is a continuous function defined for all real numbers, f(-1)=1, f(-5)=-10, and f(x)=0 for one and only one value of x, then which of the following could be that x value? a) -6 b) -5 c) -4 d) 0

19. ## algebra

2. The function f is defined as follows f(x)={4+2x if x0 a) Find the domain of the function b) Locate any intercepts c) Graph function d) Based on graph find range e) Is f continuous on its domain? a) The domain of the function f is

20. ## algebra

Find the domain and range of the relation and determine whether it is a function? Answers are Domain x>1 range y>0yes it is a function Domain all real numbers,range all real numbers yes it is a function Domain positive integers, range positive integers no

21. ## math

An equation, f, has a domain of all whole numbers and has a range of all real numbers. Does the equation represent a function?

22. ## Math

1. Find the next number in the pattern. -1, 3, 7, 11 a. 16 b.77 c.15

A.give an example of a function whose domain is {3,4,7,9}? and whose range is {-1,0,3} B.Find two different functions whose domain is {3,8}and whose range is {-4,1} C Explain why there does not exist a function whose domain is {-1,0,3} and whose range is

24. ## algebra can someone help my buddy ray out

identify the vertex and the axis of symmetry of the graph for the function y=3(x+2)^2 a.vertex(2,-3 axis of symmetry x=2 b.vertex(-2,-3) axis of symmetry x=-2 c.vertex(2,3) axis of symmetry x=2 d.vertex(-2,3) axis of symmetry x=-2 identify the maximum or

25. ## calculus help

Suppose that f'(x)= (2x^2-5x-12)/(3x^2-7x+2) and that f(x) is continuous for all real numbers x. a) Do a sign diagram to list the values of x where f(x) has local maximums and local minimums. In addition, list the intervals where f(x) is increasing and

26. ## Algebra

Given the following piecewise function f(x)= {-x+1 for x < 0 {-1 for 0 ≤ x ≤ 3 {-2x for x > 3 a) Find the domain b) Find the range c) Find the intercepts d) Is f continuous on its domain? If not, state where f is discontinuous. e) Graph the function

27. ## MATH

A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in the interval [-1, 1].

28. ## 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?

29. ## math

find the domain of the composite function fog. f(x)=x/x-2;g(x)=-8/x a. domain of fog is {x/?} b. the domain of fog is all real numbers

30. ## Algebra

What is the smallest integer value of c such that the function f(x)=x^2+1/x^2-x+c has a domain of all real numbers? Thank you!

31. ## Algebra

What is the difference between domain and range? Describe a real life situation that could be modeled by a function? I think I understand domain and range. Domain is the x axis and range is the y axis correct? I need help with applying it to real life.

32. ## algebra

An equation, f, has a domain of all whole numbers and has a range of all real numbers. Does the equation represent a function? Explain why or why not.

33. ## mark check my work algebra

a cartoonist uses the function below to calculate the net profit he earns from sellings his drawings.In the function, d represents the number of drawings he sells. N(d)= 30(d)-\$500...what is domain of N(d)? is the answer all non negative real numbers?

34. ## Algebra II

Given no other restrictions, what are the domain and range of the following function? f(x)=x^2-2x+2 A. D= all real numbers R={y|y>=1} B. R=all real numbers D={x|x>=1} I think it is A...?

35. ## URGENT ALGEBRA 2

identify the vertex and the axis of symmetry of the graph for the function y=3(x+2)^2 a.vertex(2,-3 axis of symmetry x=2 b.vertex(-2,-3) axis of symmetry x=-2 c.vertex(2,3) axis of symmetry x=2 d.vertex(-2,3) axis of symmetry x=-2 identify the maximum or

36. ## Sequence and series

Do you know the difference between a sequence and a series? Graph the terms of an arithmetic series. Remember the domain is the set of natural numbers, not the set of real numbers. What type function do you see? Graph the terms of a geometric series.

37. ## algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)?

38. ## math

1. Provide two examples of a function: (1) as a table of values and (2) as a graph. Explain the definition of a function. Be sure to include mathematical vocabulary in your response. 2. In a paragraph, explain what the domain and range is for the function

39. ## Math(Urgent)

Find the domain of the function. h(x)= 10 over x^2 - 2x I think the answer is all real numbers except 2 but I do not know if it is right!

40. ## Algebra

23. The ___ axis represents the independent variable. X? 21. Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above

41. ## math

Find the domain and range for y=x^2+9. Is the answer all real numbers? How would you enter that in interval notation? From Googling the definition of real numbers, I now understand that the infinity sign would not be included. For a continuous function you

42. ## Math

What is the domain and range fro the expentiral function f(x)=-2x4^x-1+3? Domain:all real numbers Range:all real numbers less than 3 Domain:all real numbers Range:all real numbers greater than 3 Domain: all real numbers greater than-2 Range: all real

43. ## math 116

What is the difference between domain and range? The domain of a function is the set of all values for the independent variable (in the following example, that's the x) for which the function is defined. That is, if you have a function such as f(x) = 1/x

44. ## algebra

Find the domain and range of the function. 1. f(x)= x^2-x I got: Domain= All Real Numbers Range= All Real Numbers > -1 (with a line under the greater than sign) 2. f(x)= 1-x^2 I got: Domain= All Real Numbers Range= All Real Numbers < 1 (with a line under

45. ## Math

Assume that f is a continuous function from the real numbers to the real numbers such that for all numbers x,y, and a it is true that f(x+y)=f(x) + f(y) and that f(ax)=af(x). Further assume that f(1) = pi. Find f'(-1). Please explain your reasoning. I am

46. ## Calculus (Limits)

If g(x) is continuous for all real numbers and g(3) = -1, g(4) = 2, which of the following are necessarily true? I. g(x) = 1 at least once II. lim g(x) = g(3.5) as x aproaches 3.5. III. lim g(x) as x approaches 3 from the left = lim g(x) as x approaches

47. ## Algebra :P... again

Hi! Sorry.. but 1 more question? Direction: Find the domain of the function. Problem: y = - 1 0 / 1 1 - x [A] All real numbers except x= -11 [B] All real numbers except x= 0 [C] All real numbers except x= 10 [D] All real numbers except x= 11 Also.... if

48. ## algebra

Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example.

49. ## math

The function ​f(x)​ is the number of feet below the surface of the water a diver is at x seconds. After 14 s, the diver reached the maximum distance of 22 ft below the surface of the water. The diver stayed in the water for 20 minutes. What is the

50. ## Math

For nth root functions, I know that if "n" is even, then the domain must be equal or greater than zero. If "n" is odd, then domain will be all set of real numbers. But how do I determine the range of an n-th root function?

51. ## Algebra 2 Could use help asap

I really am trying to work these problems out on my own. Please help If f(x)=3x^2 g(x)= 1/6+x find the following and give the domain (f+g) (x) (3x^2) + (1/6+x) x is all real numbers and x is not equal to 6 (f-g) (x) (3x^2) - (1/6+x) 3x^2-x-6 x is all real

52. ## College Algebra

Here is the whole question... I have figured most of it out but I need help with part (b)(f) and (g)... Maybe you also check the work I have already done Given the following function, find: (a) vertex, (b) axis of symmetry, (c) intercepts, (d) domain, (e)

53. ## College algebra

If the domain and range of a function consists of real numbers, then you can graph it by plotting all ordered pairs (x, f(x)). Remember "y" = f(x). How can you tell by looking at a graph if it represents a function?

Given the following piecewise function f(x)= {-x+1 for x < 0 {-1 for 0 ≤ x ≤ 3 {-2x for x > 3 a) Find the domain b) Find the range c) Find the intercepts d) Is f continuous on its domain? If not, state where f is discontinuous. e) Graph the function

55. ## Algebra. Formalizing relations and functions

1.Identify the domain and range of the following relation. {(3,7),(3,8),(3,-2),(3,4),(3,1)} A.Domain:{3} Range:{-2,1,4,7,8} B.Domain:{-2,1,4,7,8} Range:{3} C.Domain:{all real numbers} Range:{all real numbers} D.Domain:O/ Range:O/

56. ## Math11

Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2 − 3x + 2, [0, 2] Yes, it does not matter if f is continuous or differentiable, every

57. ## Algebra

What is the domain of y = 2/(x) + 2 x>0 x=0 All real numbers except x = 0 I think the domain is All real numbers except x = 0 Is that correct?

58. ## Algebra II

What is the domain of y = 2/(x) + 2 x>0 x=0 All real numbers except x = 0 I think the domain is All real numbers except x = 0 Is that correct?

59. ## Math

A continuous function f has domain of all real numbers. If f(-1) = 5 and f(1) = -5, explain why function f must have at least one zero in the interval [-1, 1]

60. ## MATH

A continuous function, f, has domain all real numbers. If f(-1) = 5 and f(1) = -5, explain why f must have at least one zero in the interval [-1, 1].

1. What is ((-12x^6 + x)) / ((-4x^2))? A: 3x^4 - 1/4x 2. What is the greatest common factor of the terms of the polynomial 6x^3 - 18x^2 + 12x + 3? A: 3? 3. Which is a solution to n/n+2 = -8/n? a. -4 b. -2 c. 2 d. 4 A: a? 4. Which of the following is

62. ## Math Algebra 1111

If the domain of a function F is the set of all real numbers and the domain of a function G is the set of all real numbers, under what circumstances do (F+G)(x) and (F/G)(x) have different domains? Whenever G(x) = 0 then the domains would differ. For

63. ## Algebra

The vertex of a parabola is at (-2,4), and the x-intercepts are at -6 and 2. Determine the domain and range of the function. a. D: all real numbers R: all real numbers b. D: all real numbers R: y ≤ 4 c. D: -6 ≤ x ≤ 2 R: y ≤ 4 d. D: x ≤ 4 R: all

64. ## AP Calc. AB

1.Which function is NOT continuous everywhere? A.y=(4x)/(x+1)^2 B.y=|x| C.y=(x)/(x^2+1) D.y=√(x^2+1) E.y=x^(2/3) 2.State the domain f(x)= √((x+6)) sinx 3. Let h(x) {(sin2x)/x, if x ≠ 0 {a, if x=0 find the value of a so that hi s continuousat x=0 a.

65. ## Math

Write the equation of a function with the following requirements: A domain of all real numbers over 3, a range of all real numbers, an x-intercept of (5,0), and a vertical asymptote at x = 3.

66. ## Algebra

The function 5x^2+2x-1's domain is all real numbers, according to the answer key. However, I don't know how to factor this to prove it. Could you show me? The function the sq. root of y-10 has a domain of all numbers so that y is greater than or equal to

67. ## Calculus

Describe the Domain of the Function: F(x)= 2x/(x-2)(x-1) The domain of the function consists of all real numbers x except ____?

68. ## Function Notation

Ive been shown that a function can be written like so f:X->Y,f(x)=rule where X is the Domain and Y, the co-domain. Firstly, what is the co-domain? Ive tried looking it up but all I get is "the set of which y values fall in". If that is the case, say for

69. ## Algebra2

Give the domain of the function. 1. g(x)= 5/ x^2 -25 = all real numbers 2.f(t)= 3t^2+5t+2 = Negative 3. h(x)= squareRoot of ; 5x-2 = All real numbers

70. ## algebra

the equation is f(x) = (1/sq. root of 1-x^2) 1. f(x) is never zero. 2. 0 is in the domain of f 3. All negative real numbers are in the domain of f 4. All positive real numbers are in the domain of f 5. 1 is in the domain of f 6. f(x) is never negative 7.

71. ## PRE-CALC

Determine the domain of the following function: f(x)=sqrt x-7/x^2-5x-6 I think the domain is [7,all real numbers) Can you please tell me if this is correct?

72. ## Algebra 2

Give the domain of the function. g(x)= x^3-1 I think the domain is all real numbers. Am I wrong? If so why?

73. ## Algebra

22. State the domain of the function y=3x+2 a. D: Real numbers b. D: x not equal to 0 c. D: x < 0 A? 23. State the range of the function y=2x^2 a. R: y greater than or equal to 0 b. R: x not equal to 0 c. R: y < 0 I'm not sure? 24. Is y=sqrt2x a function?

74. ## Algebra

57. Find the domain of: y= 5 _____ 2x+24 a. all real numbers except 12 b. all real numbers except 0.08 c. all real numbers except -0.08 d. all real numbers except -12 I still don't get how to do these, and this one looks even more complicated than the

75. ## math

the equation is f(x) = (1/sq. root of 1-x^2) 1. f(x) is never zero. 2. 0 is in the domain of f 3. All negative real numbers are in the domain of f 4. All positive real numbers are in the domain of f 5. 1 is in the domain of f 6. f(x) is never negative 7.

76. ## Math

The function b(h) models the percent of a certain wildflower that blooms during months in which the average daily sunlight is h hours. Name the most appropriate domain for this function. A. Integers, h ≤ 24 B. Integers, 0 ≤ h ≤ 24 C. Real numbers, 0

77. ## Math

Find the domain and range for y=x^2+9. Wouldn't the domain and range just be all real numbers since nothing else is really given in the equation? How would you enter "all real numbers" in interval notation? Would it include the infinity sign?

78. ## Algebra

Can an equation that has a domain of all whole numbers and have a range of all real numbers be a function?

79. ## Algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)? Thank you!

80. ## Algebra

How many real numbers are not in the domain of the function f(x)=(1/x-64)+(1/x^2-64)+(1/x^3-64)? Thank you!

81. ## Pre-Calculus

Which of the following statements best describes the domain of the functions sine and arcsin? A)Sine domain is all real numbers; Arcsin domain is all real numbers. B)Sine domain is restricted; Arcsin domain is all real numbers. C)Sine domain is all real

82. ## Algebra 2

A package of paper towels contains 3 rolls. Each package of paper towels costs \$2.79. A function of f(x) is written to represent the cost of purchasing. What is the practical domain for the function? All whole numbers All positive All whole numbers that

This is my last question. What is the domain of the function below? f(x)= e^(x-4)-2 I got all real numbers is that correct?

84. ## Math

Come up with an expression for a function f such that the domain of f is all real numbers, lim (f(x) = 3) as x approaches 2 and f(2) = 3.

85. ## algebra

can someone help me find the domain and range of the function f(x)=3(x-3)^2-1 I think the domain is all real numbers but I'm not sure about the range

86. ## Algebra

A package of paper towels contains 3 rolls. Each package of paper towels costs \$2.79.​ A function, f(x), is written to represent the cost of purchasing x packages of paper towels. What is the practical domain for the function f(x)? these are the options

87. ## Algebra

A package of paper towels contains 3 rolls. Each package of paper towels costs \$2.79.​ A function, f(x), is written to represent the cost of purchasing x packages of paper towels. What is the practical domain for the function f(x)? these are the options

88. ## Algebra

13. Find the domain of y=2x+1 Bobpursley said: The domain of x is not restricted by that equation. Does that mean the domain is all real numbers?

89. ## Algebra-domain

I had to find the domain of a function, and my answer is that x is all real numbers except -5 and 6. How do I write that in interval notation?

90. ## Math

Could anyone, please, help me solve this? Let f be a function with the domain the set of all real numbers except 0 and 1 ,that satifies the equation : 2xf(x) - f[(x-1)/x] = 20 Find f(5/4)

91. ## Math

Find the domain and range of the inverse f(x)=-4x-2 y=-4x-2 x=-4y-2 x+2/-4=-4y/-4 f(x)=x+2/-4 answer: domain (all real numbers) range (all real numbers)

92. ## Math

An equation, f, has a domain of all whole numbers and has a range of all real numbers. Does the equation represent a function?

93. ## Calculus

The continuity of floor functions the function: x - floor(x) it is continuous on what interval? i got all real numbers except for integers. is this right. thank you.

94. ## math 2

let f and g be two functions defined by: f(x)=x+5, with domain all real numbers; g(x)=2x, with all real numbers. which of the following statement are true for f and g?

Please check urgently .I have to submit the assignment A give an example of a function whose domain equals the set of real numbers and whose range equals the set? the set {-1,0,1} BGive an example of a function whose domain equals (0,1)and whose range

Where do I look for the domain in this- The domain of y =1/(x-6) + 3 Possible answers: All real numbers except x=6 All real numbers except x = -6 All real numbers except x=3 All real numbers except x= -3 Thank you

97. ## Math

Find the domain and range of the inverse f(x)=-4x-2 y=-4x-2 x=-4y-2 x+2/-4=-4y/-4 f(x)=x+2/-4 domain (all real numbers) range (all real numbers)

98. ## Discrete Math

Determine the domain and range of: y = 5 – [1/ (1 + x)] So, would the domain be all real numbers except -1? And would the range be all real numbers except zero? I'm really confused. . .

99. ## Math

Did I do this right? Find the domain and range f(x)=-4x-2 y=-4x-2 x=-4y-2 x+2/-4=-4y/-4 f(x)=x+2/-4 answer: domain (all real numbers) range (all real numbers)

100. ## domain

Find the domains of f and f' 1, f(x) = xe^x 2. f(x) = x^(3/5) 3. f(x) = x/(x-2) TIA 1) R 2) It's the interfal from zero to infinity for f but for f' it is this inteval with zero excluded, because unlike f, f' is singular at zero. 3) Here only the point 2