Let
f(x) = mx-12 if x is less than -5
= x^2 +5x -7 if x is greater than or equal to -5.
If f(x) is a function which is continuous everywhere, then we must have
m=_______
from f(x) = x^2 + 5x - 7
f'(x) = 2x+5
f'(-5) = -10+5 = -5
so at the transition point the slope must be -5
thus m = -5