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A function

`f(x)`

is said to have a jump discontinuity at

`x=a`

if:

`\lim_(x->a^(-))f(x)`

exists.

`\lim_(x->a^(+))f(x)`

exists. The left and right limits are not equal. Let

`f(x)={(8x-5, if x<9),((1)/(x+9), if x>=9):}`

Show that

`f(x)`

has a jump discontinuity at

`x=9`

by calculating the limits from the left and right at

`x=9`

.

```
\lim_(x->9^(-))f(x)=
\lim_(x->9^(+))f(x)=
```

Now, for fun, try to graph

`f(x)`

.