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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)?

Guest 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

 

 

cool cool cool

CPhill  Aug 23, 2018

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