Jump discontinuity, where?

• Oct 8th 2009, 10:48 AM
Raj
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 <br /> img.top {vertical-align:15%;}<br /> $b$ does <br /> img.top {vertical-align:15%;}<br /> $f$ 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.
• Oct 8th 2009, 11:14 AM
Calculus26
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
• Oct 9th 2009, 07:13 AM
Raj
I don't think i understand, wouldn't that be infinite
• Oct 9th 2009, 07:29 AM
Calculus26
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