Posted by **leticia** on Tuesday, March 1, 2011 at 12:47pm.

PLEASE I NEED HELPPPPP.. i have many exercises like that, just want to know where to start thanks.

f(x)= x^3+2x^2-x-2 / x^2+x-6

find:

1. domain

2. symmetry or not

3. determine if f(x)is: a)in lowest trem b)proper/improper

4. x-intercepts, y-intercepts

5. zeros of f(x) and their multiplicity

6. vertical asymptotes

7. ablique/horizontal asymtotes

- mth -
**Henry**, Thursday, March 3, 2011 at 11:14pm
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 long-hand 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. X-Ints = -2, -1 , 1 = roots = solu.

When X = 0, F(0) = -2/-6 = 1/3 = Y-int.

5. Zeroes = X-Ints = -2,-1, and 1.

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