F(x)= x/x^3-

By: Nicholas Gerbracht, Gaby Soto, Erica Soto, Ana Marie Llamosas
Page 396 problem #26
Process of analyzing a rational
function
Find horizontal
and Oblique
Asymptotes
Find the
intercepts
Put rational
function in
factored
form
Simplify rational fucntion into
lowest terms to find the
Vertical Asymptote
Determine
the domain
Plot the
information
on a graph
Putting the function into rational
form
The function is already
in rational form
Determining the domain
The domain is found
by finding what makes
the denominator = 0
Domain is all reals except -1 or 1
Also domain includes what the vertical
asymptotes are.
Simplifying into lowest terms
Once you factor the denominator
It is in lowest terms
Finding horizontal and Vertical asymptotes
Horizontal asymptote is N/A
because the degree of the
numerator is 1, and the degree
of the denominator is 2. Since
N<M therefor the H.A is Y= 0
Vertical asymptote are x=-1
x=1
Because those numbers
make the denominator equal
to 0.
So the graph will get close to
but never touch the x=-1
and 1
Finding the intercepts

Finding the zeros (x-intercepts)
◦ By replacing y with zero you can find the x
intercepts, i.e. the zeros
x =0
◦ x-intercept is (0,0)

Finding the y-Intercepts
◦ Replace x with zero to find the y intercepts
◦ y-intercept is at (0,0)
StepStep
3: Connect
1: Plot the
the points
dots, remember
on a graphthe asymptotes
Step 2: Plot asymptotes
Plotting the information on a graph
X
F(x)
-2
-2/3
-3
-3/8
-4
-4/15
-1/2
2/3
0
0
1/2
-2/3
2
2/3
3
3/8
4
4/15
Slide show made by
Gaby Soto
-determined horizontal/vertical asymptotesNick Gerbracht
-made the powerpointErica Soto
-X and Y intercepts and domainAna Marie Llamosas
-Points on the graph-