The only integer factors of 4 are (1)(4) and (2)(2). As symbolipoint said, by the "rational roots theorem" the only rational (in this case, integer) roots must be factors of 4: [itex]\pm 1[/itex], [itex]\pm 2[/itex], [itex]\pm 4[/itex]. It easy to try those in the polynomial and see that x= 1 makes it 0: x-1 is a factor. Trying x= -2 also gives a root so x+2 is also a factor.math4life said:Homework Statement
Y1=(x3+3x2-4)/(x2)
Homework Equations
Slant Asymptote at y=x+3. (X-1) and (X+2) appear to be intercepts in the back of the book. How do I factor the numerator to get that?
The Attempt at a Solution
I know this is simple and there is a method to find the zeros of the numerator that I am overlooking- please help.
A rational function is a mathematical expression that is written as a ratio of two polynomial functions. It can also be described as a function that can be written in the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials.
The key features of a rational function graph include the horizontal and vertical asymptotes, x and y intercepts, and any holes in the graph. These features can help determine the behavior of the function and its domain and range.
To determine the domain and range of a rational function, you need to consider the restrictions on the variable x. The domain is all the possible values of x that make the function valid, while the range is all the possible values of y that the function can output.
The horizontal asymptote of a rational function can be found by analyzing the degrees of the numerator and denominator polynomials. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. To find the vertical asymptotes, set the denominator equal to zero and solve for x.
To sketch a rational function graph, you can start by plotting the key features such as the asymptotes, intercepts, and any known points. Then, use the behavior of the function as x approaches the asymptotes to determine the general shape of the graph. You can also use a table of values to plot additional points and get a more accurate graph.