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Let \(\[f(x) = \left\{ \begin{array}{cl} ax+3, &\text{ if }x>2, \\ x-5 &\text{ if } -2 \le x \le 2, \\ 2x-b &\text{ if } x <-2. \end{array} \right.\]\)      

Find a+b if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).

 Apr 14, 2019
 #1
avatar+104648 
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We want

 

a(2) + 3  = (2) - 5           and        ( -2) - 5  = 2(-2) - b

2a +3 = -3                                     -7   = -4 - b

2a = -6                                             b = 3

a = -3       

 

a + b   =   -3 + 3   = 0

 

See the graph, here : https://www.desmos.com/calculator/fsg2n87hro

 

 

cool cool cool     

 Apr 14, 2019

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