Let\(f(x) = \left\{ \begin{array}{cl} ax+3, &\text{ if }x>2, \\ x-5 &\text{ if } -2 \le x \le 2, \\ 2x-b &\text{ if } x <-2. \end{array} \right.\) Find a+b if the piecewise function is continuous
To find a: Evaluate f(2) = 2 - 5 = -3
So: when x > 2, ax + 3 = -3
a·2 = -6
a = -3
To find b: Evaluate f(-2) = -2 = 5 = -7
So: when x < -2, 2x - b = -7
2(-2) - b = -7
-4 - b = -7
b = 3
+980 
