For what value(s) of b is this function continuous at x = 3?

Question

𝑓(𝑥) = { 𝑏𝑥 + 4 for 𝑥 ≥ 3

𝑏𝑥^2 − 2 for 𝑥 < 3

Answer 1

Plug in x=3 for both sides of f(x), set the sides of f(x) equal, then solve for b.

3b + 4 = 9b - 2

You should be able to finish from here.

Answer 2

The function is continuous at x=3 if it has the same value (or approaches the value as a limit) from both above and below x =3. In this case, just set the two parts equal at x=3 since both pieces are well-behaved:

b(3) + 4 = b(3²) - 2 and solve for b...

Take care.

Answer 3

By definition, both equations should have the same value at x = 3 to be continuous at x = 3.

First, plug 3 in the equations, and solve for b.

3b + 4 = 9b - 2

b = 1