[PDF] Graphing Rational Functions.ks-ia2

What are the features of a rational function?

Two important features of any rational function r(x)= p(x) q(x) r ( x) = p ( x) q ( x) are any zeros and vertical asymptotes the function may have. These aspects of a rational function are closely connected to where the numerator and denominator, respectively, are zero.

How to graph a rational function?

Now, compare the numerator and denominator degrees to determine the slant or horizontal asymptotes. Finally, you can sketch the graph you wanted to. Let us learn graphing simple rational functions via an example. Example: Sketch a graph for the function, f (x) = (x + 2) (x – 3)/ (x + 1)2 (x -2) .

Is a polynomial a rational function?

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. No, its a rational function. The numerator and the denominator are polynomials though.

Why do we study rational functions in school?

The interest in rational functions, as far as school mathematics is concerned, is twofold: they are only one step away from polynomials and are therefore worth knowing, and surprisingly, their graphs display features that are genuinely different from those of polynomials—they have asymptotes—and are therefore instructive for that reason.