Question

Describe the vertical asymptote(s) and hole(s) for the graph of

posting pic

Answer 1

i was hopen you cn haha

Answer 2

So first of all you have vertical asymptotes at x=1 and x=5 because both of those would make the denominator 0, which isn't possible. Then you have a hole at x=1, because x-1 can be crossed out of both the denominator and the numerator, and when you set it equal to 0, you get x=1. Then if you want to find the y coordinate of the hole, plug x=1 into (x-3)/(x-5), which is what you have leftover once you cancel out x-1

Answer 3

asymptote: x = –5 and hole: x = –1 this one ?

Answer 4

there's another asymptote at x=1

Answer 5

asymptote: x = 5 and hole: x = 1

Answer 6

The denomenator (the bottom part o f fraction) can never ever have a zero. In your example if x=1 then (1-1)(1-5) = (0)*(-4) which would make it zero or undefined at 1. Similarly, if x=5 you get the results where there is a zero in the denominator. So we can see that in this function x can never = 1 or 5. Another part of retricemtotes is that as the value of x gets smaller and smaller approching 0 but never reaching and because its in the denomenator, the whole number gets bigger and bigger to infinity. Example.:
5/0.5= 10, 5/0.2=25, 5/0.1=50..... 5/.000000001=50,00000000!

Answer 7

On a side note, that expression also has a horizontal asymptote, y = 1.