SOLUTION: how do i analyze a rational function?

Question 985083: how do i analyze a rational function?

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Analyzing the graph of a rational function
step 1: Find the domain of the rational function
step 2: Write R in lowest terms (simplify the rational function if possible)
step 3: Locate the intercepts of the graph.
step 4: Test for symmetry
step 5: Locate the vertical asymptotes
step 6: Locate the horizontal or oblique asymptotes
step 7: Determine points, if any, where the graph crosses the asymptotes
(horizontal or oblique)
here is an example:

analyze the graph of a rational function

step 1: Find the domain of the rational function
domain is:
{ | and
step 2: Write R in lowest terms (simplify the rational function if possible)

step 3: Locate the intercepts of the graph.

-> y-intercept is at (,)

-> x-intercept is at (,)
step 4: Test for symmetry
if the function has symmetry about the y�-axis
find

so, => symmetry
and , the function has symmetry about the origin

step 5: Locate the vertical asympthote
=> and are the vertical asympthotes
for next step:
Horizontal and Oblique Asympthote reminder(the degree of the numerator is
and the degree of the denominator is )
1.
If , then is a proper fraction and will have the horizontal asympthote .
2.
If , then R is improper and long division is used.
(a)
If , the quotient obtained will be a number, and the line y = is a horizontal asymptote.
(b)
If , the quotient obtained is of the form (a polynomial of degree 1), and the line is an oblique asymptote.
(c)
If, the quotient obtained is a polynomial of degree 2 or higher and R has
neither a horizontal nor an oblique asymptote.
Horizontal asymptote:
as ->�
so, horizontal asymptote is
no oblique asymptotes found
step 7: Determine points, if any, where the graph crosses the asymptotes

graph:

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