SOLUTION: How do i graph the Asymptote ? y = 1/x = -3

Question 619268: How do i graph the Asymptote ?
y = 1/x = -3
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
not sure what your equation is.
could be:
y = (1/x) - 3)
or could be:
y = (1/(x-3)
i'll assume y = 1/(x-3)
this will have a vertical asymptote at x = 3.
that's when the denominator goes to 0.
when x is smaller than 3, the graph will be negative
when x is larger than 3, the graph will be positive.
when x is smaller than 3, it will become more and more negative as you get closer to 3.
when x is larger than 3, it will become more and more positive, the closer you get to 3.
the graph will look like this:

if you were to draw a vertical line at x = 3, you would see that each asymptote approaches that vertical line but never quite touches it.
the following graph simulates that as best i can do with algebra.com graphing software.

if you were to manually plot the graph, you would pick values of x that have less and less intervals between them the closer you get to 3.
something like:
values of x for:
2, 2.5, 2.8, 2.9, 2.95, 2.98, 2.99, 2.995, etc.
coming from the other end, you would have values such as:
3.005, 3.01, 3.02, 3.05, 3.1, 3.2, 3.5, 4
the graph will rise dramatically in either positive or negative direction the closser you get to x = 3.

RELATED QUESTIONS
How do I graph y = x + 1/x And how do I know where the asymptote/s is/are???... (answered by richwmiller)

How do I graph {{{y=-log(3,x+1)}}} I know the domain is (1, infinity) and range is all... (answered by Alan3354)

How do I graph y= -2.3 as its horizontal... (answered by stanbon)

How to identify and graph the asymptote and y intecept for graphing exponential growth. (answered by drk)

How do I graph {{{y=3 Ln x-2}}} I know the vertical asymptote is x=-2 but I have no idea... (answered by lwsshak3)

Graph y=(1/3)^x. Identify the domain, asymptote, and range. Did I do this right? x=3... (answered by jim_thompson5910)

Equation of a hyberbola (x-3)^2 over 4 - (y+2)^2 over 9 = 1 How do I find the... (answered by lwsshak3)

What is the asymptote and graph of: y= (1/(x+2)) +... (answered by belle3833)

Describe the vertical asymptote(s) and hole(s) for the graph of y = (x - 3)(x - 1)/(x (answered by lwsshak3)