# Math Help - Jump discontinuity, where?

1. ## Jump discontinuity, where?

Code:
Given this piecewise function
f(x)=
-x+b if x<-2
5 if x=-2
((-5)/(x-b))+4 if x>-2

For what value(s) of

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$b$ does

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$f$ have a (finite) jump discontinuity at −2? Write your answer in interval notation.
I've been able to find the removable and infinite discontinuity and where it is continuous, but i've no idea how to find the interval where there is a jump.

2. The answer is all values of b except -2,3

since if lim f(x) is from the left exists
2+ b = 5 b= 3

Similarly if -5/(-2-b) + 4 = 5 then b = 3 makes the limit from the right

3. I don't think i understand, wouldn't that be infinite

4. If b = -2 then the right hand limit at -2 is infinite

If b =3 we have removed the discontinuity at -2

For any other value of b we have different right hand and left hand limits
(but both are finite) hence we have a jump discontinuity