# find the constants a and b so the function is continuous on a real line piecewise function: f(x)={5, if x3+ is -5. I don't know how to find the constants

122,972 results
1. ## 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

2. ## Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a and b #2. Let h be a

3. ## 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

4. ## Functions - math

The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a and b ii) Find the

5. ## 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

6. ## 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

7. ## 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

8. ## calculus

Find the constant a such that the function is continuous on the entire real line g(x)=x^2-a^2/x-a if x doesn't equal a 6 if x=a

9. ## Calculus (Continuity)

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0

10. ## 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

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.

12. ## CALCULUS

For the piecewise function, find the values g(-8), 8(3), and g(8). g(x)={X+6,FOR X3

13. ## 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].

14. ## 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

15. ## math

For each piecewise function, find the specified function values. g(x)={x+4, for x1 g(-4),g(0),g(1), and g(3)

16. ## calculus

1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2. a. Find an expression for y’ b. Write an equation for

17. ## calculus

find the constants a and b so the function is continuous on a real line piecewise function: f(x)={5, if x3+ is -5. I don't know how to find the constants

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 (urgent!)

A line has the equation x = my + b for some real nonzero constants m and b. a. In terms of m and/or b, what is the x-intercept of this line? b. In terms of m and/pr b, what is the slope of this line? I have no idea how to solve this, so please walk me

20. ## Continuity Calculus Help

Find the value of constants c and d that make the function below continuous at x = 4. f(x) = x2 − 3x x < 4 c x = 4 d + x x > 4 c = d = 8 I got d=8, but finding c is giving me trouble.

21. ## Calculus

Find the constants a and b such that the function is continuous on the entire line f(x){7, x is less than or equal to -3 ax+b, -3 is less than x is greater than 4 -7, x is less than or equal to 4

22. ## calculus

Let f be the function defined by f(x)= sqrt(x), 0

23. ## Pre-Calc 12

Let f(x)=a(x-p)^2+q be a quadratic function, where a,p,q are constants and a≠0. f(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define g(x) be the function after performing all the

24. ## Math (Semicircle)(Pre-calc)

goo.gl/photos/e6Ks3v4Qqj177Nun6 The graph below is made from two semicircles. The domain of the function in the graph is [−8,8] [-8,8] . Find a piecewise formula for the function f(x) f(x). Help please, I already on my last attempt and any help is

25. ## Algebra

Given the following piecewise function: Find the Given the following piecewise function: f(x)= {?(x+10 for -9 ?x

26. ## mathematics

Is the following piecewise function continuous at x = 3? Y = 2x3 − 5, for x > 3 Y = 5x2 + 4, for x ≤ 3

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 constant a such that the function is continuous on the entire real line. f(x) = 5x^2, x ≥ 1 ax − 3, x < 1 ???Please, thnks.

30. ## Calculus

For the following function, find the values of the constants 𝑎 and 𝑏 for which the function is continuous, but not differentiable. 𝑓(𝑥)={𝑎𝑥+𝑏,𝑥>0 & sin𝑥,𝑥≤0.

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

32. ## math-calculus

the absolute value function g(x) = |5-x| can be written as a piecewise function. the piecewise function which represents g(x) is this have to be g(x) = x-5 if x be greater to or equal to five. and the negative piece have to be 5-x. does it matter if i

33. ## pre calc

The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of x dollars. T(x) = (i) Determine whether T is continuous at 6061. (ii) Determine whether T is continuous at 32,473. (iii) If T had discontinuities, use

34. ## AP Calculus

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

35. ## calculus

find the constants a and b so that the function is continuous on the entire real line. F(x)= 3, x≤-1 ax+b, -1

36. ## Math - Continuity

Determine the constants a and b so that the function f is continuous on the entire real line: f(x) = 2 , x=

37. ## calculus

find the constants a and b so that the function is continuous on the entire real line. F(x)= 3, x≤-1 ax+b, -1

38. ## Calculus

I'm having a little trouble with this problem...it would be great if you could point out where I'm going wrong. Hours of Daylight as a Function of Latitude. Let S(x) be the number of sunlight hours on a cloudless June 21st, as a function of latitude, x,

39. ## Math -- Calculus

Hours of Daylight as a Function of Latitude Let S (x) be the number of sunlight hours on a cloudless June 21, as a function of latitude, x, measured in degrees. (a) What is S (0)? (b) Let x0 be the latitude of the Arctic Circle (x0 ≈ 66◦ 30′ ). In

40. ## Math

Create a function that closely gives the graph given in the link. The function may be a piecewise function but it does not necessarily have to be a piecewise function. a. Give a brief narrative explaining what you did to create your function. b. List your

41. ## 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].

42. ## Calculus

A(x)= |4-3x| A'(x)={ ,if x4/3 I have to try to find the derivative of this function using a piecewise function and I'm a bit confused about how to do so. Could someone explain how?

43. ## calculus

1. Let y = f(x) be the continuous function that satisfies the equation x^4-5x^2y^2+4y^4=0 and whose graph contains the points (2, 1) and (-2, -2). Let l be the line tangent to the graph of f at x = 2. a. Find an expression for y’ b. Write an equation for

44. ## Calculus

consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the t -value where the function is not continuous. I say continous, am I wrong? If I am wrong what interval is it

45. ## College Algebra

A clothing store is having a sale on t-shirts: Buy 4 shirts at full price, then every subsequent shirt is half off. The total amount a customer spends on x shirts can be modeled by the piecewise function below: T(x) = 28x for 0 ≤ x ≤ 4 14x + 56 for x >

46. ## Calculus

If f(x) is a continuous function, find the constants a and b such that f(x) = { -x -3

47. ## math -- Calc

1. A car travels 20 mi/hr for 2 hours and then 30 mi/hr for 3 hours. a) For 0

f(x)=|x|+1 Let A(r) be the enclosed by the x axis, the line x=-2, the graph of the function f, and the line x=r for any r=>-2 A) Write A(r) as a piecewise function with its joints at r=0 Please walk me through each step i am really confused!!

49. ## Math

flickr.(dotcom)/photos/77304025@N07/6782789880/ Create a function that closely gives the graph given below. The function may be a piecewise function but it does not necessarily have to be a piecewise function. a. Give a brief narrative explaining what you

50. ## Calculus

flickr.(dotcom)/photos/77304025@N07/6782789880/ Create a function that closely gives the graph given below. The function may be a piecewise function but it does not necessarily have to be a piecewise function. a. Give a brief narrative explaining what you

51. ## Calculus (Continuity)

If the following function is continuous, what is the value of a + b? f(x) = {3x^2 - 2x +1, if x < 0 a cos(x) + b, if 0

52. ## Calculus

consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the t -value where the function is not continuous. The function is not continous and it is not continous on 7

53. ## calculus

find the tangent function is continuous on the interval (-90,90) but is not uniformly continuous

54. ## Math

Problem 3. Probability Density Functions 2 points possible (graded, results hidden) For t∈R, define the following two functions: f1(t)=1/√2πexp(−max(1,t^2)^2) and f2(t)=1/√2πexp(−min(1,t^2)^2). In this problem, we explore whether these

55. ## Calculus

How do I find local minimums based on f'(x) with line segments? I have a picture of a graph with a the points (-4,0), (-3,2.5), (0,0), (2,2), and (5,0). Here is the question: The graph of f ' (x), the derivative of f(x), is continuous for all x and

56. ## 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

57. ## calculus

given the following piecewise function x+11 for -9

58. ## precalculus

(A) find the domain of the function, (B) decide if the function is continuous, and (c) identify your horizontal and vertical asymptotes. F(x)= (3x^2+1)/(x^2+x+9) Find the zeros (if any) of the rational function. G(x)= (x^3-8)/x^2+4 H(x)=5 + 3/(x^2+1) G(x)=

59. ## 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.

60. ## math

Each of the following statements is false. Provide why the statement is false. 1) Every function that is continuous at x=a is differentiable at x=a. 2) The tangent line to y=f(x) when x=x0 is given by y=fprime(x0)x+f(x0). 3) The linerization of a function

61. ## Math--Calculus

Let y = f(x) be the continuous function that satisfies the equation x^4 - (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for y'. (b) Write an

62. ## calculus

Find the constants a & b such that the function f(x)={2 if ≤ -1 {ax+b if -1

63. ## Calculus

f'(x) if x is less than or greater than 1 Let F'(x)={ g'(x) if x>1 Where f'(x)=x/(x^2-2)^2 and g'(x)=3x-4 A. If f(1)=3/2, find f(x) B. If F(x) is continuous at x=1, find g(x). C. Express F(x). D. If F(x) is continuous at x=1, determine if F(x) is

64. ## Calculus

find the value of a, if it exists, such that the following function is continuous at X = 2. piecewise function f(x)={x^2-3x+1, if x>2; a, if x=2; 3-2x, if x

65. ## 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

66. ## help college algebra

given the following piecewise function f(x) = -x+1 for x

1. A car travels 20 mi/hr for 2 hours and then 30 mi/hr for 3 hours. a) For 0

Find a function f(x), perhaps a piecewise function that is defined but not continuous on (-infinity, infinity) for which the function lf(x)l is both defined and continuous on (-infinity, infinity). f(x)= lf(x)l =

69. ## 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.

70. ## Calculus

I need help creating an equation for a piecewise defined function with two different rules, that is continuous but not differentiable at the point where the rules change, x=3. Please help to justify the answer.

71. ## Help me check my calculus questions

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

72. ## College Algebra

Create a piecewise function of the following scenario where Upper D left-parenthesis t right-parenthesis is the total distance walked (in miles) as a function of time t (in minutes): “You begin a walk from your home at a fast pace of 3 miles per hour for

73. ## Math (Calc.)

1.Use the IVT to explain why the following is true. If f continuous on (a,b) and f(x) does not equal to zero for all x in the interval (a,b), then f(x) > for all x in the interval (a,b) or f(x) < 0 for all x in the interval (a,b). 2. You are given that a

74. ## Calculus

Find all values of a, B so that the function f(x)=1 if x>3, f(x)=ax-10 if x

75. ## 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

76. ## 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]

77. ## Math

Can someone please help me with piecewise functions. I know what they are but when it gets to advanced i have ttrouble. s(x)= /x-2/ + /x-3/ + /x+1/ (/ / = 'modulus') Write as a piecewise defined function. Have no idea tbh. Thanks

78. ## using a ti 89

i am attempting to graph the piecewise function y=(-2/3)x-6 if -9

79. ## Calculus

consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the t -value where the function is not continuous. Is the t value 0

80. ## 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

81. ## algebra

Suppose f(x)=Ax+B for real constants A and B. If f(60)=70 and f(72)=79, find k such that f(k)=k. PLEASE HELP :] Ok we have f(x)=Ax+B which is a line. We also know (1) f(60)=70 which means A*60+B=70 (2) f(72)=79 " " A*72+B=79 Which means A*12=9 if we

82. ## 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

83. ## Math

For t∈R, define the following two functions: f1(t)=12π−−√exp(−max(1,t2)2) and f2(t)=12π−−√exp(−min(1,t2)2). In this problem, we explore whether these functions are valid probability density functions. Determine whether the function f1

84. ## Math

For this equation, x is real, b and c are each real constants, and b is less than c. Find the possible values of y so that y = (x^2-bc)/(2x-b-c)

85. ## 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

86. ## Calculus

COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the x -value where the function is not continuous. Is is continous? If not? what interval then?

87. ## Calculus

COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the x -value where the function is not continuous. Is is continous? If not? what interval then?

88. ## Calculus

COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the x -value where the function is not continuous. Is is continous? If not? what interval then?

89. ## Math / Algebra

Can you check my work? Thank you :) 1. The Domain of a function F is the same as the range of F^-1 (True or False?) Answer: True. 2. Does the function y = |x-2| have an inverse? Select the best answer. A. Yes, it passes the horizontal line test. B. No, it

90. ## mathamatics

on december31, 1995, paul invested \$2000 in a stock. his stocker gains 20% ever odd month (jan, march, may..) and loses 15% every even month (feb, april, june...) it says write a piecewise defined function for the value of the stocker n months after the

91. ## Calculus

Piecewise function problem. Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x

92. ## math

You are given that a function f is defined and continuous at every real number x except x=2. Also, f(x)=0 precisely for x=1 and 7. Finally, you know that f(-3)=4, f(1.5)=2, f(4)= -3, and f(10)=6. Solve the inequality f(x) > 0.

93. ## math

express y=0.1(1000)^x in the form lg y =mx+c ,where m and c are constants ,and x is a function of x . Determine the constants m and c and the function x .

94. ## math

Let f be he real-valued function defined by f(x)=sin^3x+sin^3|x| (a) find f'(x) for x>0 (b) find f'(x) for x

95. ## math

1. (1 pt) Let g(y) = 8y2 + 13y + 5. A function f is known to be continuous on ( −∞, ∞), to satisfy g ◦ f (x) = 0 for all real x and it is known that the value f (8) is not equal to −1. You have enough information to determine f precisely.

96. ## Calculus

consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval? If it is continuous, type "continuous". If not, give the t -value where the function is not continuous. I say continous, am I wrong? If I am wrong what interval is it

97. ## precalculus

(A) find the domain of the function, (B) decide if the function is continuous, and (c) identify your horizontal and vertical asymptotes. F(x)= (3x^2+1)/(x^2+x+9) Find the zeros (if any) of the rational function. G(x)= (x^3-8)/x^2+4 H(x)=5 + 3/(x^2+1) G(x)=

98. ## algebra

For given the following piecewise function find the domain and range F(x) ={ 2x + 4 for x< -3} {-1 for -3-¡Ü x ¡Ü4} {- x 1 for x > 4}

99. ## math

how do i find the rule of a piecewise linear function?