The general form of a rational function is p ( x) q ( x), where p ( x) and q ( x) are polynomials and q ( x) 0. In other words, there must be a variable in the denominator. STEP 4: Find $x$ and $y$ intercepts of the graph of $f$.īelow are shown the graph of the given function $f$ (green), the x-intercept (red), the y-intercept (brown), the horizontal asymptote (dashed blue) and the vertical asymptote (dashed red). A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1. It is given by the zero of the denominator if it is not equal to the zero of the numerator. STEP 1: Use the fact that division by zero is not allowed to find the domain of $f$. When there are common linear factors in the numerator and denominator, the graph will be the graph of the simplified function after cancellations, but with missing points at the zeros of the denominator. There is a graph at the bottom of the page that helps you further understand the solution to the question show below. Solve each step below then click on "Show me" to check your answer. (Recall that the denominator cannot equal zero) (2) Find vertical asymptote(s) by setting the denominator equal to zero and solving.
METHOD: Given a Rational Function ( ) ( ) Qx P x y, where P(x) and Q(x) are polynomial functions (1) Determine domain. Graphs of rational functions (old example) Graphing rational functions 1. Graphs of rational functions: vertical asymptotes. To graph a rational function, you find the asymptotes and the intercepts, plot a few points, and then sketch in the graph.
The given function f(x) = x 2 / (x 2 - 1) hasĢ vertical asymptotes at x = 1 and x = -1 and a horizontal asymptote at y
If you examine the 4 graphs given above only graph b has a vertical asymptote at x = 1 and a horizontal asymptote at y = 2.Įxample 2 : Identify the graph of the function f(x) The given function f(x) = 2x/(x - 1) has a vertical asymptote at x = 1 and a horizontal asymptote at y = 2. You may want to go through tutorials on graphing and rational functions before starting this tutorial.Įxample 1 : Identify the graph of the function f(x)
It is 'Rational' because one is divided by the other, like a ratio. Example 7.3. A function that is the ratio of two polynomials. In this first example, we see a restriction that leads to a vertical asymptote. In the next two examples, we will examine each of these behaviors. The graph will exhibit a hole at the restricted value. The vertical and horizontal asymptotes are shown in broken lines. The graph of the rational function will have a vertical asymptote at the restricted value. Them is the possible graph corresponding to the given function. This is a tutorial on identifying the graph of a rational