Question

hard question:

Answer 1

ok, tell me what function has a vertical asymptote x=0 (the y-axis) and horizontal asymptote y=0 (the x-axis) ?

Answer 2

or, at least try to think of the SIMPLEST example of a function where \(x\ne0\).

Answer 3

alright here: a rational function

Answer 4

good, but give me a specific function pliz.

Answer 5

ok

Answer 6

1/x

Answer 7

yes, y=1/x is good

Answer 8

\(\large\color{black}{ \displaystyle {\rm f}(x)=\frac{\rm 1}{x} }\)

Answer 9

in this function \(x\ne0\), and thus, \(x=0\) is the vertical asymptote of this function.

Answer 10

now, will this function ever have a y-value of 0?

Answer 11

yes. I think because of the 1

Answer 12

no, because 1/x is never going to be 0, for any value of x.

(and if x is 0, then it's undefined)

Answer 13

and since y is never equal to 0 therefore horizontal asymptote is \(y=0\)

Answer 14

so then yes it will have a value of 0

Answer 15

no, it won't have a a value of y=0, because 1/x is same as y and 1/x is never zero

Answer 16

ok, y=1/x will be something like this