Rational Function Worksheet 2
1. Graph the rational function
Name:
5x2 + 10x
5x2 − 15x − 20
Factor the numerator and denominator.
Implied Domain:
Vertical Asymptotes:
x-intercepts:
In between x−intercepts and vertical asymptotes:
Far left and far right:
Put it together:
2. This example is a special case (not in our textbook):
x2 − x − 2
x3 − 3x2 − 4x − 12
Factor the numerator and denominator.
Implied Domain:
Check if the expression may be simplified.
Holes: The special detail of this example is a hole. Note how the common factor of
(x − 2) appears on top and on bottom. In the simplified form of the rational function
x = 2 gives a function value (a y value) that makes sense. x = 2 is still not in the
domain, so the point (2, f (2)) is marked with an open hole. Mark this as a point
instead of a vertical line.
Vertical Asymptotes:
x-intercepts:
In between x−intercepts and vertical asymptotes:
Far left and far right:
Put it together: