SOLUTION: draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2

Question 615579: draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
draw asymptotes (if any), to graph the rational function, plot at least 2 points on each piece of the graph x^2+5x+5/x+2
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I don't have the means to plot a graph for you, but I can provide information with which you can plot the curve yourself.
When degree of numerator is one unit higher than that of the denominator, you will have slant or oblique asymptotes, as in this case.
To find equation of slant asymptote, divide numerator by denominator by long division or synthetic division. The quotient is the equation of the slant asymptote.
(x^2+5x+5)/(x+2)=(x+3)+remainder=1
equation of slant asymptote: y=x+3
..
To find vertical asymptote, set denominator=0, then solve for x
x+2=0
x=-2=vertical asymptote
..
y-intercept
set x=0,then solve for y
f(0)=(x^2+5x+5)/(x+2)=5/2
y-intercept=5/2
..
x-intercepts
set y=0
x^2+5x+5=0
solve by quadratic formula:
x=-3.62 and -1.38
..
number line
<....-.....-3.62...+...-2...-...-1.38...+....>
see graph below:

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