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avatar+254 

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).

 Jul 22, 2020
 #1
avatar+30929 
+1

If the curve is continuous then we must have:

 

At x = 2:   a*2 + 3 = 2 - 5  or 2a = -6   so a = -3

 

At x = -2:  2*(-2) - b = -2 - 5   or  -4 - b = -7  so  b = 3

 Jul 22, 2020
 #2
avatar+254 
+1

How do we find the equation of a continuous piecewise function though?

 

Thank you very much! 

 Jul 22, 2020
 #3
avatar+30929 
+1

Well, given a and b we can write   

 

Alan  Jul 22, 2020
 #4
avatar+254 
+1

Thank you!

 Jul 22, 2020

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