Piecewise functions

Let:

f₁(x)  =  ax + 3

f₂(x)  =  x + 5

f₃(x)  =  2x - b

 

If the function is continuous, that means  f₁(2)  must equal  f₂(2)  and also that  f₃(-2)  must equal  f₂(-2)

 

f₁(2)  =  f₂(2)

a(2) + 3  =  2 + 5

2a + 3  =  7

2a  =  4

a  =  2

 

f₃(-2)  =  f₂(-2)

2(-2) - b  =  -2 + 5

-4 - b  =  3

-b  =  7

b  =  -7

 

And so

 

a + b  =  2 + -7  =  -5

 

Check: https://www.desmos.com/calculator/xdgxm9i5yb

Hi Hectictar,

It is really good to see you here  :)