Expert: Sherman D. - 1/30/2008

Question
QUESTION: i am having a lot of trouble with horizontal asymptotes and vertical asymptotes.in some problems it asks to sketch the graphs of rational functions like 1/x+2.then check for any intercepts or asymptotes.im not sure how to look for that.what am i looking for?

ANSWER: to find vertical asymptotes is easy. Whenever you have a value in the denominator, just set it equal to 0. Whatever answer you get will be your vertical asymptote.

no as far as finding the horizontal asympote, just switch the x and y value, then solve for y.

y = 1/(x + 2)
x = 1/(y + 2)
x(y + 2) = 1
y + 2 = (1/x)
y = (1/x) - 2

so x cannot be equal to 0

ANS:
VA = -2
HA = 0

---------- FOLLOW-UP ----------

QUESTION: thank you!that actually helped me a lot on my test today!!what about finding the zeros of polynomial functions??could you give me a step by step process on that???thanks!

Answer
ax^2 + bx + c = 0
use the quadratic formula. its the conclusion to completing the square.

x = (-b ± sqrt(b^2 - 4ac))/(2a)

if you have

ax^3 + bx^2 + cx + d = 0

then try group factoring like this

(ax^3 + bx^2) + (cx + d) = 0
x^2(ax + b) + (cx + d) = 0

in short, if ax + b and cx + d after you have divided cx + d and ax + b by a number that they can both be divided by and if the result makes them have the same identical factor after them, then you can combine them to give you 2 factors, if they can't have identical factors, then check with answers.yahoo.com for help.

if you can give me some problems, i can probably help you further.