Vertical, Horizontal and Oblique Asymptotes of Rational Functions—In Depth
{"Image DocumentName": "Vertical, Horizontal and Oblique Asymptotes of Rational Functions\u2014In Depth", "Image ImageDescription": "We\u2019ve learned when vertical, horizontal and oblique asymptotes will exist and how to find them (if they do exist). We will discuss now what exactly they are and what they do. This goes back to the aged-old question: What is an asymptote? Most people will say: An asymptote is a line that a curve is approaching, but never touch it. This definition is not exactly accurate. The curve can actually touch the asymptote, and as many times as it wants. See graph on the right. Fortunately, the graph above isn\u2019t a rational function since the graph of a rational function. 1. can never touch its vertical asymptote(s), and. 2. will not touch its horizontal (or oblique) asymptote as it\u2019s approaching it, but it can touch it when it isn\u2019t approaching it. x. y. Vertical Asymptotes. A vertical asymptote is a vertical line that determines the behavior of the graph of a rational function as it is approaching to an x-value at which the function is undefined. Example 1: x R(x) Horizontal Asymptotes and Oblique Asymptotes. A horizontal asymptote is a horizontal line (and an oblique asymptote is a slant line) that determines the end behavior of the graph of a rational function (i.e., as x becomes very large (approaching \uf0a5) or very small (approaching \u2013\uf0a5)). Example 1: Example 2: x. \u2013\uf0a5 \u20131000. \u2013100. \u2013 \uf0a5 R(x) x. \u2013\uf0a5 \u20131000. \u2013100. \u2013 \uf0a5 R(x) x + 2.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}