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# Piecewise-Defined Functions

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For real numbers $x$, let

$f(x) = \left\{ \begin{array}{cl} x+2 &\text{ if }x>3, \\ 2x+a &\text{ if }x\le 3. \end{array} \right.$

What must the value of $a$ be to make the piecewise function continuous (which means that its graph can be drawn without lifting your pencil from the paper)?

Feb 24, 2021

At $3$, it must be continuous. So $2*3+a=3+2\implies \boxed{a=-1}$.