DDesmos SAT Prep
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Rational Functions & Asymptotes

Read vertical and horizontal asymptotes straight off the graph.

The Desmos trick

Graph the rational function. Desmos renders a visible gap or dashed-looking break at vertical asymptotes, and you can zoom out far to see the curve flatten toward its horizontal asymptote.

  • Type the function as a fraction: y = (x+3)/(x-5)
  • Zoom in near suspected vertical asymptotes — the graph shoots off toward infinity
  • Zoom out (scroll out repeatedly) to see the horizontal asymptote the curve approaches

Practice questions

Q1What is the equation of the vertical asymptote of f(x) = (x + 3)/(x - …
Medium
Q2As x approaches infinity, the function f(x) = (6x^2 + x - 1)/(2x^2 - 5…
Medium
Q3What is the equation of the vertical asymptote of f(x) = (2x - 7)/(x +…
Medium
Q4As x approaches infinity, the function f(x) = (4x^2 - 1)/(2x^2 + 5) ap…
Medium