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avatar+359 

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).

MIRB16  Aug 28, 2017
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2+0 Answers

 #1
avatar+78618 
+2

 

We need to find values for "a"  and "b"  that will make the graph continuous

 

First, let  x  = -2

And solve this for :b"

 

-2 - 5  =2 (-2) - b

-7 = -4 - b

-3  = -b

b  = 3

 

Next, let x  = 2  

And solve this for "a"

 

2 - 5  + a(2)  + 3

-3  = 2a + 3

-6  = 2a

a = -3

 

So  we have that

 

                  -3x + 3, if x > 2    

f(x)  =            x - 5,  if  -2 ≤ x ≤ 2

                   2x - 3, if x < -2

 

Here's the graph from left to right :  https://www.desmos.com/calculator/ibd5jn8m8s   

 

 

 

cool cool cool               

CPhill  Aug 28, 2017
edited by CPhill  Aug 28, 2017
 #2
avatar+359 
+4

Thank you!

MIRB16  Aug 28, 2017

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