SOLUTION: Hi I need help with this problem please! The problem is f(x)=(x^2-2x+5)/(x+3) I need to know: Holes? Vertical asymptote(s)? Horizontal asymptote(s)? Slant asymptote(s)?

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Question 741394: Hi I need help with this problem please!
The problem is f(x)=(x^2-2x+5)/(x+3)
I need to know:
Holes?
Vertical asymptote(s)?
Horizontal asymptote(s)?
Slant asymptote(s)?
y-intercept?
x-intercept?
And a sketch of the graph.
thank you!!
Answer by josgarithmetic(39625) (Show Source):
You can put this solution on YOUR website!
I will tell you just this much:

It appears to not have any hole, since the numerator is not perfectly divisible by the denominator. There is a vertical asymptote at , because that is where the function is undefined, since denominator would be zero.

Try performing the division. There will be a remainder. The quotient portion is the slant asymptote. Use synthetic division:

-3____|____1_____-2_____5
______|___________-3____15
__________________________
______|____1_____-5_____20
_________ ___ x-5_________remainder 20

The slant asymptote would be