Vertical asymptote  Rational Functions
Vertical asymptote
Basic concepts:
 Factoring trinomials
 Factoring difference of squares: $x^2  y^2$
Related concepts:
 Infinite limits  vertical asymptotes
Lessons
Notes:
For a rational function: $f(x) = \frac{numerator}{denominator}$
Provided that the numerator and denominator have no factors in common (if there are, we have “points of discontinuity” as discussed in the previous section), vertical asymptotes can be determined as follows:
$\bullet$equations of vertical asymptotes: x = zeros of the denominator
$i.e. f(x) = \frac{numerator}{x(x+5)(3x7)}$; vertical asymptotes: $x = 0, x = 5, x = \frac{7}{5}$

1.
Graphing Rational Functions
Sketch each rational function by determining:
i) vertical asymptote.
ii) horizontal asymptotes

2.
Identifying Characteristics of Rational Functions
Without sketching the graph, determine the following features for each rational function:
i) point of discontinuity
ii) vertical asymptote
iii) horizontal asymptote
iv) slant asymptote