+0  
 
0
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3
avatar+229 

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).

 Mar 5, 2021
 #1
avatar+30523 
+2

The line of the graph needs to be continuous so

at x = 2        ax+3 has to equal   x-5

                      ax+3 = x-5

                       ax = x - 8      at x= 2

                        a(2) = 2-8

                          a = -3

 

 

and   at  -2          x-5   has to equal 2x-b

                            x-5 = 2x-b

                            b+5 = x                for x = -2

                             b+5 = -2

                             b = -7

 Mar 5, 2021
 #3
avatar+30523 
+1

*** corrected  ***

Had an incorrect '+' sign:

 

and   at  -2          x-5   has to equal 2x-b

                            x-5 = 2x-b

                            b - 5 = x                for x = -2

                             b - 5 = -2

                             b = 3

ElectricPavlov  Mar 5, 2021
 #2
avatar+229 
0

thats wrong but thanks

 Mar 5, 2021

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