Part 2/5:
is a simple example of a rational function where ( x ) cannot equal zero, as it would result in division by zero.
Graphing Rational Functions
When graphing rational functions, the behavior around the undefined points is crucial. For the function ( f(x) ) mentioned above, the graph will demonstrate asymptotic behavior as the values of ( x ) approach zero from either side.
A more complex example is
[
f(x) = \frac{2x^4 - x^2 + 1}{x^2 - 4}
]
In this case, the denominator ( x^2 - 4 ) equals zero when ( x = \pm 2 ), indicating that the graph will have vertical asymptotes at these points. A plot of this function will visually illustrate its behavior near these critical points.