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Rational expressions

Features of rational expressions/ hyperbola

  • As these expressions have a function in the denominator, this function can have a zero value, making the expression undefined.
  • When the function is undefined, there can be an asymptote, or a missing value(s).
  • An asymptote is a straight line, which the curve approaches but never reaches.
  • A specific type of rational function is a hyperbola and has the general form \[ y = \frac{c}{x-a} + b\] 
  • When \(x\) approaches \(a\), \(y\) tends to \(+\infty\) or \(-\infty\). Under such conditions we say the curve has a vertical asymptote at \(x = a\).
  • As \(y\) approaches \(b\), \(x\) tends to \(+\infty\) or \(- \infty\) and thus the curve has a horizontal asymptote at \(y = b\).
  • An example is given below