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