SOLUTION: Find the slant asymptote of the graph of the rational function and graph it F(x)=x^2-x-6/x-4 2. Determine the symmetry of the graph of f Find the y-intercepts Find the

Question 674471: Find the slant asymptote of the graph of the rational function and graph it
F(x)=x^2-x-6/x-4
2. Determine the symmetry of the graph of f
Find the y-intercepts
Find the x-intercpts
Find the vertical asymptote(s)
Find the Horizontal asymptote
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the slant asymptote of the graph of the rational function and graph it
Use synthetic division to find the quotient
4)....1....-1....-6
......1....3....|..6
slant asymptote = x+3
=================================
F(x)=x^2-x-6/x-4
Factor:
F(x) = [(x-3)(x+2)] / (x-4)
----------
2. Determine the symmetry of the graph of f
f(-x) = [x^2 +x -6] / (-x-4)
----
f(x) does not equal f(-x) so no y-axis symmetry.
-----
-f(-x) = [x^2+x-6] /(x+4)
---
f(x) does not equal -f(-x) so no origin symmetry.
=========================================================
Find the y-intercepts
Let x = 0, then y = -6/-4 = 3/2
------------------------
Find the x-intercpts
Let y = 0, solve [(x-3)(x+2)] = 0
x = 3 or x = -2
-----------------------
Find the vertical asymptote(s)::::
Solve x+4 = 0
x = -4
--------
Find the Horizontal asymptote:::::none because degree of numerator is
greater than degree of denominator.
==================
Cheers,
Stan H.
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