+230 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).
+36916 The line of the graph needs to be continuous so
at x = 2 ax+3 has to equal x-5
ax+3 = x-5
ax = x - 8 at x= 2
a(2) = 2-8
a = -3
and at -2 x-5 has to equal 2x-b
x-5 = 2x-b
b+5 = x for x = -2
b+5 = -2
b = -7
+36916 *** corrected ***
Had an incorrect '+' sign:
and at -2 x-5 has to equal 2x-b
x-5 = 2x-b
b - 5 = x for x = -2
b - 5 = -2
b = 3
