SOLUTION: Find the slant asymptote of the graph of the rational function and b. f(x)=x^2+x-2/x-3 b.) Use the slant asymptote to graph the rational function. ** determine the symmet

Algebra ->  Rational-functions -> SOLUTION: Find the slant asymptote of the graph of the rational function and b. f(x)=x^2+x-2/x-3 b.) Use the slant asymptote to graph the rational function. ** determine the symmet      Log On


   

Question 971228: Find the slant asymptote of the graph of the rational function and b.
f(x)=x^2+x-2/x-3
b.) Use the slant asymptote to graph the rational function.
** determine the symmetry of the graph of f
** find the y-intercepts
** find the x-intercepts
** find the vertical asymptote
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
A matter of polynomial division; the quotient is the slant asymptote and the remainder will tend toward 0 as x goes to the left or right unbounded.


Choosing synthetic division,

_________3_________|_________1________1________-2
___________________|
___________________|_________________3________12
___________________________________________________
____________________________1________4________10

Remainder is 10; which would represent 10%2F%28x-3%29.
The slant asymptote is highlight%28y=x%2B4%29.

y-intercept? Let x=0 and evaluate f.

x-intercepts? Check for roots of the numerator.
Discriminant, 1-4%28-2%29=9;
x=%28-1%2B-+3%29%2F2
x=-2 or x=1/2.

Vertical asymptote? Where is the function undefined?