In order for the function to be continuous at x = -7, the limits from either side as x approaches -7 must be equal:
[tex]\displaystyle \lim_{x\to-7^-} f(x) = \lim_{x\to-7}(x^2-12x+16) = 149[/tex]
[tex]\displaystyle \lim_{x\to-7^+} f(x) = \lim_{x\to-7}(kx+268) = -7k+268[/tex]
Solve for k :
149 = -7k + 268
7k = 119
k = 17
