Question

Explain why each function is discontinuous at the given point. f(x) = x/x - 1 at x = 1

Answer 1

so what is discontinuous?

Answer 2

you mean the word discontinuous or?

Answer 3

yeah

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

@zepdrix can u help?

Answer 8

\[\large f(x)=\frac{x}{x-1}\]

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.

Answer 9

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

Answer 10

infinite right? lol

Answer 11

yes good c:

Answer 12

ok thanks

Answer 13

Good Good.