Answer:
k ≈ 1.88
Step-by-step explanation:
In order for the function to be continuous, the pieces of the function must have the same value at x=3. That is ...
f(3) = 3(3) +k = k(3^2) -6
15 = 8k . . . . . add 6-k, simplify
k = 15/8 = 1.875 ≈ 1.88
To two decimal places, the value of k that makes f(x) continuous at x=3 is 1.88.
