a zero denominator means that the line is vertical

Question

dumbcow · Answer

it means the function is undefined at that point

dumbcow · Answer

or yes the slope could be seen as a vertical line

nowhereman · Answer

The result of dividing through zero can not be defined consistently. A vertical line is not the graph of any function. So you can not talk about slope.

anonymous · Answer

A zero denominator means that the function is undefined. It has no slope.

anonymous · Answer

Which is different from having a slope of zero. Basically dividing by zero is a no-no.

dumbcow · Answer

Also a zero denominator shows where a vertical asymptote is defined which is usually referred to as an imaginary vertical line

nowhereman · Answer

This statement lacks mathematical rigour. First of all a vertical asymptote is not part of the function. Also not everywhere where there occurs a zero denominator there has to be a vertical asymptote (see x/x for example which can be extended continuously in zero) and not everywhere where there is a vertical asymptote, do you have a zero denominator. (take ln x for example with a vertical asymptote at x = 0)