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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)?

 Apr 20, 2021
 #1
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The value of a is 3.

 Apr 20, 2021
 #2
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Incorrect, Sorry.

Guest Apr 20, 2021
 #3
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at x = 3   both pieces must have the same value to be continuous

 

x+2   =   2x + a    when   x = 3

3+2   =  2(3) + a

5   = 6 + a

a = -1

 Apr 20, 2021
 #4
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Correct \(a=-1\)

Guest Apr 20, 2021

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