A rational function is a function that can be written in the form of f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials. In other words, it is a function that is the ratio of two polynomial functions.
The domain of a rational function is the set of all real numbers except for those values of x that make the denominator Q(x) equal to zero. These values are called the vertical asymptotes of the function.
To simplify a rational function, factor both the numerator and denominator, and then cancel out any common factors. This will result in a simplified form of the function.
Rational functions can have both vertical and horizontal asymptotes. The vertical asymptotes occur when the denominator of the function is equal to zero, while the horizontal asymptotes occur when the degree of the numerator and denominator are equal. The horizontal asymptote can also be found by dividing the leading coefficients of the numerator and denominator.
To find the x-intercepts, set the function equal to zero and solve for x. To find the y-intercept, substitute in x = 0 and solve for y. Keep in mind that rational functions may not have x-intercepts, but they will always have a y-intercept at (0, c), where c is the constant term in the function.