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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)?

Aug 23, 2018

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

Let x  = 3  and set the functions equal.... we have

3 + 2  = 2(3) + a

5  = 6 + a

5 - 6  = a

- 1  =  a

See the graph  here  that shows that this value of a makes the function continuous :

https://www.desmos.com/calculator/ux7xrnhaxi

Aug 23, 2018