rational function help please please!!?

Question

Given the following rational function:

f(x)= 4x^2-10x+6 / -2x+3

oh, oops, i forgot,

Find the vertical and horizontal asymptotes.

Answer 1

4x^2-10x+6=2(2x^2-5x+3)=2(2x-3)(x-1)

so the function becomes:
(2(2x-3)(x-1))/(3-2x)

the top part can be multiplied by -1 to flip one of the roots
we will choose to flip the (2x-3) into (3-2x)
just remember to put a - out in front to cancel out multiplying by -1

-2(3-2x)(x-1)/(3-2x)=
-2(x-1)

x cannot be equal to 3/2
this makes a hole(not an asymptote) at x=3/2

there are no horizontal or oblique or vertical asymptotes

Answer 2

There is no horizontal asymptote because the degree of the numerator is higher than the degree of the denominator (there is a slant asymptote though). The vertical asymptote comes from value for x which makes the denominator equal zero. So
-2x + 3 = 0
3 = 2x
3/2 = x

VA: x = 3/2

Answer 3

In mathematics, a rational function is any function whose output can be given by a formula that is the ratio of two polynomials. ("Rational function" suggests a function of rational numbers onto the set of rational numbers. A constant function such as f(x) = π may be a "rational function" in this context even though it is in fact irrational. "Polynomial ratio" or "polynomial quotient" are more descriptive terms than the standard usage.) For a function of one variable, x, any rational function can be expressed as

f(x) = P(x)/Q(x)
Rational function of degree 2 :
y = (x²-3x-2)/(x²-4)where P and Q are polynomials in x and Q is not the zero polynomial. The domain of f does not contain any number a for which Q(a) = 0.

A rational expression is a quotient of polynomials, sometimes called an algebraic fraction. A rational equation is an equation in which two rational expressions are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.

These objects are first encountered in school algebra. In more advanced mathematics they play an important role in ring theory, especially in the construction of field extensions. They also provide an example of a nonarchimdean field" (see Archimedean property) and an alternative construction for hyperreal number systems used in infinitesimal calculus and nonstandard analysis.

[edit] Examples
Rational function of degree 3 :
y = (x^3-2x)/(2(x^2-5))The rational function is not defined at .

The rational function is defined for all real numbers, but not for all complex numbers, since if x were plus or minus the square root of negative one formal evaluation would lead to division by zero.

The limit of the rational function as x approaches infinity is .

Try using www.wikipedia.com

Answer 4

what do you want us to do with that function? be more specific