mth
posted by leticia .
PLEASE I NEED HELPPPPP.. i have many exercises like that, just want to know where to start thanks.
f(x)= x^3+2x^2x2 / x^2+x6
find:
1. domain
2. symmetry or not
3. determine if f(x)is: a)in lowest trem b)proper/improper
4. xintercepts, yintercepts
5. zeros of f(x) and their multiplicity
6. vertical asymptotes
7. ablique/horizontal asymtotes

We have a fraction in which a cubic Eq is the numerator and a Quadratic Eq is the denominator. Let's factor both.
Find a value of X that gives 0 out when
plugged into the cubic Eq. It was found
by trial and error that 2 will give
an output of 0 and,therefore, satisfies
the Eq.
X = 2,
X + 2 = 0. Using longhand division,
divide the cubic Eq by x + 2 and get:
X^2  1.
(X + 2)(X^2  1) = 0,
(X + 2)(X + 1)(X  1) = 0 = numerator.
Factor the denominator and get:
(X  2)(X + 3) = 0. Therefore,
F(x)=(X + 2)(X + 1)(X 1)/(X 2)(X + 3)
The domain = all real values of x
that does not make the denominator = 0.
2 and 3 will make the denominator = 0
and are outside the domain.
1. So the domain = all real values of X
except 2 and 3.
3. a. Not in lowest term as given.
b. Proper fraction.
4. XInts = 2, 1 , 1 = roots = solu.
When X = 0, F(0) = 2/6 = 1/3 = Yint.
5. Zeroes = XInts = 2,1, and 1.