1. ## Continous Functions

hi,
can someone please explain to me the concept of continuity?..... when they say determine the values of x for which a function is continous..what do they mean and how is it done? ..thanks

2. continuous just means that the graph is connected.

e.g. if you have a piece meal function:
x - 1 for x> 0
and x for x< 0

There is discontinuity at x =0, as there are no values for x = 0.

also, if you have a hyperbola like y = 1/x. It is discontinuous when x = 0, as there is an asymptote there.

to find continous/discontinous points:

continous: occurs when there is no gap in the curve. Find the values for which x cannot be equal to. e.g. $\displaystyle \sqrt{x-2}$ x -2 >> 0. x must be greater or equal to 2. and hence, the curve is continuous when x is >>2.

3. Originally Posted by differentiate
continuous just means that the graph is connected.
Not exactly. You mention yourself that the hyperbola $\displaystyle xy=1$ is discontinuous at 0, but its graph is connected.

4. Originally Posted by Bruno J.
Not exactly. You mention yourself that the hyperbola $\displaystyle xy=1$ is discontinuous at 0, but its graph is connected.
What he said is : continuous => connected.
it doesn't mean that connected => continuous

And for this function, if you look at the graph on the whole domain, it's not connected at all... (negative vs. positive domain)