Rational functions are algebraic expressions that can be written as the ratio of two polynomials. In the AHL (Additional Higher Level) 2.13 topic, we focus on two specific forms of rational functions:
Where $a$, $b$, $c$, $d$, and $e$ are constants, and $x$ is the variable.
These forms are more complex than the simpler rational functions covered in SL 2.8, which typically involve linear expressions in both numerator and denominator.
Rational functions often have asymptotes, which are lines that the graph of the function approaches but never quite reaches. There are three types of asymptotes:
For the function $f(x) = \frac{2x+1}{x^2-1}$:
Intercepts are points where the function crosses the x-axis (x-intercepts) or y-axis (y-intercept).
For $f(x) = \frac{x^2-4}{x-2}$:
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