## anonymous 3 years ago Explain why each function is discontinuous at the given point. f(x) = x/x - 1 at x = 1

1. anonymous

so what is discontinuous?

2. anonymous

you mean the word discontinuous or?

3. anonymous

yeah

4. anonymous

well it means having a gap... missing doesn't continue

5. anonymous

i don't get it. why would this function be discontinuous

6. anonymous

because its saying that at point 1 it breaks its doesnt continue the line, so you have to explain why? why it broke?

7. anonymous

@zepdrix can u help?

8. zepdrix

$\large f(x)=\frac{x}{x-1}$ In the land of math, we are never allowed to divide by 0. If we let $$x=1$$, it turns the denominator into $$0$$. Which gives us a fraction of the form $$\dfrac{1}{0}$$, which is no beuno!! See how we're dividing by 0? So we say that the function is undefined, or in other words, has a discontinuity at x=1.

9. zepdrix

If we were to look at it graphically, it forms an asymptote at x=1. Remember what type of discontinuity that is?

10. anonymous

infinite right? lol

11. zepdrix

yes good c:

12. anonymous

ok thanks

13. anonymous

Good Good.