+0  
 
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avatar+147 

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
 #1
avatar+421 
+1

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

 Feb 24, 2021

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