How To Find Holes In A Graph

If a graph has a horizontal asymptote of y k then part of the graph approaches the line y k without touching it y is almost equal to k but y is never exactly.

This leaves a literal hole in the line of the graph that is often represented by an open circle. To find the asymptote divide the numerator by the denominator. Find the hole if any of the function given below. Factor the numerator and denominator of the rational equation by using trinomial greatest common factor grouping or difference of squares factoring.

So there is no hole for the given rational function. The graph of a rational function usually has vertical asymptotes where the denominator equals 0. Graphing a rational function 1 find any holes. A rational function will either have a horizontal or slant asymptote but not both.

Instead you find the slant asymptote equation in this case y x 1 and you draw that in for the rational graph. Graphing rational functions with holes. To find the coordinates of the holes set each factor that was cancelled equal to solve and substitute back in to. The only difference between the slant asymptote of the rational function and the rational function itself is that the rational function isn t defined at x 2.

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Just ignore the remainder. The quotient is the equation for the slant asymptote. An asymptote is a line that the graph of a function approaches but never touches. So the hole will appear on the graph at the point a b.

Plot the holes as open circles. In the given rational function clearly there is no common factor found at both numerator and denominator. Asymptotes and holes summary asymptotes and holes. Examples example 1.

To find the holes in the graph look at the denominator factors that were cancelled. A rational function is a quotient of two functions. Finding and graphing a hole often involves simplifying the equation. We offer a large amount of good reference tutorials on subject areas starting from basic algebra to synthetic division.

Learn how to find the vertical horizontal asymptotes of a function.