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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).

 Feb 4, 2021
 #1
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0

a + b = (-4) + (-1) = -5.

 Feb 4, 2021
 #2
avatar+116126 
+1

We want to  first  assume that

 

ax + 3    =  x   -5       when  x  =  2    so

 

a(2) + 3  =   2 - 5

a(2)  =  -3 - 3

a(2)  =  -6

a  =  -3

 

Likewise.....we want to assume that

 

x-  5 =    2x  - b  when  x  =  -2

 

-2  -5  = 2(-2) - b

 

-7  = -4   -   b

 

b =  -4 +  7

 

b =  3 

 

a + b   = 0

 

See the graph here :  https://www.desmos.com/calculator/zh7glvlbum

 

 

cool cool cool

 Feb 4, 2021

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