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f(x) = ax + 3 if x > 2,

f(x) = x + 5 if -2 <= x <= 2,

f(x) = 8x + b if x < -2

 

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 12, 2021
 #1
avatar+12741 
+2

Hello Guest!

 

The graph is continuous when a = 0 and b = - 9.

laugh !

 Jul 12, 2021
 #2
avatar+32779 
+4

To find the value of a that makes the curve continuous at the upper intersection, set x = 2 in the upper two expressions and equate them:

i.e.   a*(2) + 3 = (2) + 5

or   2a+3 = 7

      a = 2

 

Similarly to find the value of b that makes the curve continuous at -2, set

 (-2) + 5 = 8*(-2) + b

 

I'll let you finish.

 Jul 12, 2021

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