Hello tutors please help with the following question:

note* this isn't for an assignment but rather for my own comprehension and understanding! Thank you.

State whether each of the following functions are continuous or not for all values in their domain. Justify your answer. Complete parts (a) through (d). (a) a(t) = altitude of a skydiver t seconds after jumping from a plane. Choose the correct answer below. O A. The function a(t) is discontinuous because the skydiver's parachute slows him down. O B. The function a(t) is continuous because the skydiver's altitude decreases as time increases, with no breaks in between. O C. The function a(t) is continuous because the skydiver's altitude remains constant. O D. The function a(t) is discontinuous because the skydiver's altitude is constantly changing.Determine the intervals on which the following function is continuous. p(x) = 3x4 +6x2- 8 The function is continuous on the interval(s). (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)Determine the intervals of continuity for the following function. Choose the correct answer below. a O A. [-4, - 3), [-3, - 2). [- 2, - 1]. ( -1, 0] O B. [-4, - 3], ( - 3, - 2). (- 2, - 1). (-1, 0] O C. [-4, - 3). [-3, - 2). (-2, - 1). (- 1, 0] O D. (-4, -3). (- 3, - 2), (-2, - 1). (-1, 0)5x +7x if x 5 a. Determine the value of a for which g is continuous from the left at 5. b. Determine the value of a for which g is continuous from the right at 5. c. Is there a value of a for which g is continuous at 5? a. The value of a for which g is continuous from the left at 5 is (Simplify your answer.)Classify the discontinuities in the function h(x) = x"- 7x + 10x at the points x = 0 and x = 9. x(x - 9) The function has at x = 0 and at x = 9. an infinite discontinuity a jump discontinuity a removable discontinuityDetermine whether the following function is continuous at a. Use the continuity checklist to justify your answer. f(x) = 4x-8;a=1 Select all that apply. A. The function is continuous at a = 1. B. The function is not continuous at a = 1 because f(1) is undefined. C. The function is not continuous at a = 1 because lim ((x) does not exist. x-1 D. The function is not continuous at a = 1 because lim ((x) # f(1). x-1Determine the value of the constant a for which the function f(x) is continuous at - 1. x-+ 3x + 2 f(x) = if x - 1 x + 1 if x = - 1 The function f(x) is continuous at - 1 when a = . (Type an integer or a fraction.)Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer. 3x + 8x + 4 f(x) = ., a =7 x2-7x Select all that apply. A. The function is continuous at a = 7. B. The function is not continuous at a = 7 because f(7) is undefined. C. The function is not continuous at a = 7 because lim f(x) does not exist. *+7 D. The function is not continuous at a = 7 because lim f(x) # f(7).Determine whether the following function is continuous at a. Use the continuity checklist to justify your answer. -9 if x 3 ((X)= x- 3 18=3 10 if x = 3 Select all that apply. A. The function is continuous at a = 3. B. The function is not continuous at a = 3 because ((3) is undefined. C. The function is not continuous at a = 3 because lim f(x) does not exist. D. The function is not continuous at a = 3 because lim f(x) # f(3). x-+3Determine the points at which the function f to the right has discontinuities. For each point state the conditions in the continuity checklist below that are violated. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. 3. lim f(x) = f(a) (the value of f equals the limit of f at a). X-+a f(x) is discontinuous at x =]. (Use a comma to separate answers as needed.)Determine the intervals on which the following function is continuous. f(x ) = x- 7x + 10 x2- 4 On what interval(s) is f continuous? (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)(a) Sketch the graph of a function that is not continuous at 2, but is defined at 2. (b) Sketch the graph of a function that is not continuous at 2, but has a limit at 2. (a) Which of the following graphs shows a function that is not continuous at 2, but is defined at 2. O A. OB. O c. OD.Determine the points at which the function f below has discontinuities. For each f(x) is discontinuous at x = point state the conditions in the continuity checklist that are violated. In order for f (Use a comma to separate answers as needed.) to be continuous at a, the following three conditions must hold. 1. f(a) is defined (a is in the domain of f). 2. lim f(x) exists. x-a 3. lim f(x) = f(a) (the value of f equals the limit of f at a). X-a ax3- 7x2+ 10x Classify the discontinuities in the function h(x) = at the points x = 0 and x = 9. x(x - 9) The function has at x = 0 and at x = 9. an infinite discontinuity a removable discontinuity a jump discontinuityGive the three conditions that must be satisfied by a function to be continuous at a point. Select all that apply. A. lim f(x) # f(a) X-8 [ B. lim f(x) = f(a) X-8 C. lim f(x) exists. D. f(a) is defined