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.

atx' for x 3 Let f be the function defined above, where a is a constant. For what values of a, if any, is f continuous at z = 3? A 0 only @ 3 only C 0and 3 D There is no such a.Which of the following functions are continuous on the interval 0 0. (a) Show that fis continuous at x = 0. BIUX XOCOBED 0 / 10000 Word Limit (b) For x 0, express f(x) as a piecewise-defined function. Find the value of x for which f(x) = -3. BIUX XOCOED 0 / 10000 Word Limit (c) Find the average value of fon the interval [-1, 1]. BIU X XOCOEED 0 / 10000 Word LimitLet fbe the function given by f (@) = 2 x-2 Which of the following is true? A limf (x) = I-+2' B fhas a removable discontinuity at x = 2. C fhas a jump discontinuity at x = 2. D fhas a discontinuity due to a vertical asymptote at x = 2.sin a for a 0 Let f be the function defined above, where k is a constant. (a) For what value of k, if any, is f continuous at x = -2? Justify your answer. B 0 / 10000 Word Limit (b) What type of discontinuity does f have at z = 0 ? Give a reason for your answer. B 0 / 10000 Word Limit (c) Find all horizontal asymptotes to the graph of f. Show the work that leads to your answer. B 0 / 10000 Word LimitThe graph of a function f is shown above. Which of the following statements about f is false? A fis continuous at X = a. B fhas a relative maximum at x = a. c x=a is in the domain of f. (D lim f (x) is equal to lim f (x) (E lim f (x) existsx2 + b' for a 2 Let f be the function defined above, where b is a constant. For what values of b, if any, is f continuous at z = 2? A 0only B 2 only 0 and 2 D There is no such b.Which of the following functions is not continuous on the interval -OO