Let

f(x) = x+ 3 if x > 3

f(x) = x - 6 if -3 <= x <= 3

f(x) = 3x + b if x < -3.

Find a + b if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).

Where is a?

Anyways, when x approaches -3, the value of f(x) should approach -3 - 6 = -9 from the right.

If f(x) is continuous, then the value of f(x) should approach -9 from the left too.

Then

\(\displaystyle\lim_{x\to -3} (3x + b) = -9\\ -9 + b = -9\\ b = 0\)