For the function
g|x|=2x/3x3-x2 ,find the domain,
x-intercepts, y-intercepts, critical numbers, extrema, holes,
vertical asymptotes, horizontal asymptotes, points of inflection.
If any of these items do not exist, explicitly state so.
Find the vertical asymptotes (if any) of the graph of the
function. (Use n as an arbitrary integer if necessary. If
an answer does not exist, enter DNE.)
h(x) =
x2 − 9
x3 + 3x2 − x − 3
(line in the middle of both functions is a division line)
Find all horizontal and vertical asymptotes (if any). (If an
answer does not exist, enter DNE. Enter your answers as a
comma-separated list of equations.)
r(x) =
2x − 3
x2 − 4
Part A. Find the horizontal and vertical asymptotes of ?(?)=
(6x^2) / (7(x^2 + 8))
Part B. Find the horizontal and vertical asymptotes
of ?(?)= (x^2 - 3) / (x^2 + 2x - 8)
Part C. Find the horizontal and vertical asymptotes of ?(?)=
(x^2 - 49) / (3x^2 - 75)
Part D. Find the horizontal and vertical asymptotes of ?(?)=
(x^3 - 6) / (x^2 + 14x + 49)
Explain the difference between finding the horizontal and
vertical asymptotes.
When will there be a point of discontinuity?
What could the graph look like when there is no horizontal or
vertical asymptotes.
Determine the x- and y-intercepts (if any), and vertical and
horizontal a symptotes of the rational function r, given by
r(x) =3x^2+ 18x+ 24 / x^2−3x+ 2
and then use this information to sketch a graph ofr. As part of
your analysis, you should explicitly examine the behaviour of the
function on both sides of each vertical asymptote, and evaluate the
function at appropriate test points.
1. Is it possible for a rational function to have no vertical
asymptotes? If yes the how? If no then why?
2. What is the fundamental difference between a rational
function and a polynomial function?
3. Can a rational function have no x - intercepts? If so then
how?
4. Can a rational function have two y-intercepts? Why or why
not?
5. Can the graph of a rational function cross the vertical
asymptote? Why or why not?
Please TYPE out...
Consider the function f(x) =
1/x2−5x+ 6
i. Find the equations of the vertical asymptotes.
ii Find the equations of the horizontal asymptotes.
Please explain the horizontal asymptotes clearly