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Rational functions

Asymptotes, holes and domain — where a fraction of polynomials blows up.

A rational function is one polynomial over another. Where the denominator is zero the function has a vertical asymptote (or a hole, if the factor cancels); the degrees decide the horizontal or slant asymptote. Cancelling common factors first is what separates the two cases.

דוגמה עובדת: y = 1/(x^2 - 1)

Algebra · Functions

Graph and analyse 1/(x^2 - 1)

y = \frac{1}{x^{2} - 1}

צעד אחר צעד

  1. \frac{1}{x^{2} - 1}

    An expression in x. Here is what it does.

  2. \frac{1}{\left(x - 1\right) \left(x + 1\right)}

    Factored form.

  3. \frac{d}{dx} = - \frac{2 x}{\left(x^{2} - 1\right)^{2}}

    Derivative (slope).

גלה את התשובה
\frac{1}{x^{2} - 1}

נסה את שלך.

יותר בפנים. Precalculus

Complex numbersPolynomial functionsSequences and seriesThe binomial theoremConic sectionsVectors