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Let [tex] \[f(x) = \left\{
\begin{array}{cl} ax+3, &\text{ if }x\ \textgreater \ 2, \\
x-5 &\text{ if } -2 \le x \le 2, \\
2x-b &\text{ if } x \ \textless \ -2.
\end{array}
\right.\] [/tex]

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

Respuesta :

konrad509

[tex] \displaystyle
\lim_{x\to-2^-}f(x)=2\cdot(-2)-b=-4-b\\
\lim_{x\to-2^+}f(x)=-2-5=-7\\\\
-4-b=-7\\
b=3\\\\
\lim_{x\to2^-}f(x)=2-5=-3\\
\lim_{x\to2^+}f(x)=a\cdot2+3=2a+3\\\\
2a+3=-3\\
2a=-6\\
a=-3\\\\
\boxed{a+b=-3+3=0}
[/tex]

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