URGENT HELP NEEDED ASAP
PHOTO ATTACHED
CALCULUS

Option A

Step-by-step explanation:

From the piecewise function given in the picture,

f(x) = k³ + x     If x < 3

     =    If x ≥ 3

Here, function is discontinuous at x = 3

If the function is continuous at x = 3 then,

k³ + 3 =

(k³ + 3)(k² - 3) = 16

k⁵ - 3k³ + 3k² - 9 = 16

k⁵ - 3k³ +3k² - 25 = 0

By using a graphing tool we can get the point where k = 2.081.

Option A is the answer.