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 (which means that its graph can be drawn without lifting your pencil from the paper).
+128408 We want to first assume that
ax + 3 = x -5 when x = 2 so
a(2) + 3 = 2 - 5
a(2) = -3 - 3
a(2) = -6
a = -3
Likewise.....we want to assume that
x- 5 = 2x - b when x = -2
-2 -5 = 2(-2) - b
-7 = -4 - b
b = -4 + 7
b = 3
a + b = 0
See the graph here : https://www.desmos.com/calculator/zh7glvlbum
