Contact The Learning Centre

# 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