Continuous Functions

Question

Let f(x) = {7x-5 if x < -4

{-8x+b if x ≥ -4

If f(x) is a continuous function everywhere, then we must have...

b =

Answer 1

The limit of f(x) as x approaches -4 from the left is 7(-4) - 5 = -33; as x approaches -4 from the right, f(x) approaches -8(-4) + b = 32 + b. If f is continuous everywhere, it must be continuous at x = -4, so -32 + b = 33, or, b = 65.