1. Domain of Rational Functions
Rational functions are fractions. Therefore, how would you find restrictions on your domain?
1) 2)

2. Transformations of Rational Functions
Translations, dilations, and reflections of which basic function? 3) 4)

3. X-intercepts of Rational Functions
Set the numerator equal to zero and solve.
5) 6)

4. Y-intercepts of Rational Functions
The ratio of the numerator’s constant and the denominator’s constant.
7) 8)

5. Vertical Asymptotes of Rational Functions
Set the denominator equal to zero and solve.
9) )

6. Horizontal Asymptotes of Rational Functions
3 cases…
If the numerator’s degree is lower than the denominator’s degree, the horizontal asymptote is y = 0.
If the numerator’s degree is equal to the denominator’s degree, the horizontal asymptote is y = ratio of the leading coefficients.
If the numerator’s degree is greater than the denominator’s degree, there is no horizontal asymptote.
11) 12) 13)

7. Slant Asymptotes of Rational Functions
***If there is no horizontal asymptote, then check for a slant asymptote. Specifically, if there is a difference of one degree, we can find a slant asymptote. ***
14) )

8. End Behavior of Rational Functions
End behavior in rational functions is defined by the horizontal or slant asymptotes.
16) )