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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).

 Feb 12, 2022
 #1
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Set the first two equations equal

 

ax + 3   =  x + 5

Let x  = 2

2a  + 3  =   2 + 5

2a  + 3   = 7

2a = 7 - 3

2a  = 4

a = 4/2  = 2

 

Set the second and third equations equal

x + 5  =  8x + b

Let x  = - 2

-2 + 5  =  8(-2) + b

3  = -16  + b

b = 16 + 3  = 19

 

So   the sytem that makes these continuous is

 

y= 2x + 3     ( x > 2)

y = x + 5       [ -2, 2 ]

y  = 8x  + 19    ( x < -2 )

 

a + b =   2 + 19   =  21

 

See the graph here : https://www.desmos.com/calculator/ywwaz4mykn

 

 

cool cool cool

 Feb 12, 2022

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