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