How are discontinuities created in a rational expression?

Question

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

Recall that you cannot divide by zero. This means zero cannot be in the denominator. Try it out with a calculator and see what it says

Try out 1/0 or 2/0 or any number over 0. Make sure you don't do 0/0

Because you cannot divide by zero, this is where the discontinuities come from. For example, in 1/(x+5) the discontinuity happens at x = -5 because this x value makes the denominator zero. Any other x value is valid to plug in.

jim_thompson5910 · Answer

what results visually is something like this https://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/19a33c71-9b5b-43e2-9991-4b83a699e02a.gif that red dashed line is known as the asymptote. The graph (black curve) cannot touch it. It can only get closer and closer to it