Rational function with a hole and dotted asymptotes

An example figure from the Coordinate Grid Generator.

A coordinate grid from −6 to 6 with the rational function y = (2x² + 3x − 2)/(x² + x − 2) in green, an open circle for its hole at (−2, 5/3), and dotted asymptotes at x = 1 and y = 2 — A coordinate grid numbered from −6 to 6 on both axes with the rational function y = (2x² + 3x − 2)/(x² + x − 2) drawn in green. It factors as (2x − 1)(x + 2)/((x − 1)(x + 2)), so it has a hole at (−2, 5/3), drawn as an open circle, where x + 2 cancels; a vertical asymptote at x = 1 and a horizontal asymptote at y = 2, drawn as dotted lines, with the curve in two branches on either side. Use it for holes versus vertical asymptotes, limits and end behavior.

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Answer key

y = (2x² + 3x − 2)/(x² + x − 2)

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