find values of a and k that make this function continuous

Question

f(x)=

(x^2-144)/ (x-12)  x≠a

k                           x=a

Answer 1

Factor each:  (x² - 144)/(x - 12) = (x - 12)(x + 12)/(x - 12) = x + 12.

 

What this means is that there in a hole in the graph at x = -12.  Therefore, the graph is continuous everywhere except at x = 12.  The graph will appear to be the line y = x + 12, but won't exist at x = 12.