SOLUTION: Show work please. find the slant asymptote of the graph of the rational function and Use the slant asymptote to graph the rational function. f(x)= x^2-x-20 --------

Question 714176: Show work please.
find the slant asymptote of the graph of the rational function and Use the slant asymptote to graph the rational function.
f(x)= x^2-x-20
-------------------------
x-6
b.) first determine the symmetry of the graph of f.
c.) find the x and y-intercepts
d.) find the asymptotes.
thanks!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find the slant asymptote of the graph of the rational function and Use the slant asymptote to graph the rational function.
f(x)= (x^2-x-20)/(x-6)
f(x)=(x-5)(x+4)/(x-6)
..
b.) first determine the symmetry of the graph of f.
Graph has no symmetry as can be seen by the graph below.
..
c.) find the x and y-intercepts
y-intercept:
set x=0
y-intercept=-20/-6=10/3
..
x-intercept:
set y=0
x^2-x-20
(x-5)(x+4)=0
x-intercepts at 5 and-4
..
d.) find the asymptotes.
vertical asymptote:
set denominator=0, then solve for x
x-6=0
vertical asymptote: x=6
..
slant asymptote:
divide numerator by denominator:
(x^2-x-20)/(x-6)=(x+5)+remainder
slant asymptote: y=x+5
..
number line
<...-....-4....+.....5....-.....6....+.....>

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