1. Polynomial

2. • An expression or equation that is the sum of monomials •An expression or equation having many (poly) terms

3. Rational Function

4. • A function that is the ratio or division of two polynomials

5. Asymptotes

6. • Lines that graphs approach, but never touch

7. Vertical Asymptote (VA)

8. • Vertical line(s) that graphs approach, but never touch • After you factor a rat’l function and reduce, VA’s come from factors in the denominator that DO NOT reduce/cancel. •Set those factors = 0 and solve for x. x=that value(s) will be your VA

9. Holes

10. • Point(s) in graphs that are undefined. • After you factor a rat’l function and reduce, holes come from factors in the denominator that DO reduce/cancel. •Set those factors = 0 and solve for x. There will be a hole where x = that number.

11. Horizontal Asymptote (HA)

12. • HA’s are line(s) that graphs approach, but never touch • These lines show the end behavior of graphs on the left and right sides. •In a rational function, after reducing, if a denominator exists, there is a HA in 2 cases: 1. The denominator’s greatest exponent is > the numerator’s greatest exponent. In this case, the HA is always y=0 2. The denominator’s greatest exponent = the numerator’s greatest exponent. In this case, the HA is the ratio of the coefficients of your greatest terms.

13. Slant Asymptote (SA) of Oblique Asymptotes

14. • Slant line(s) that graphs approach, but never touch • These lines show the end behavior of graphs on the left and right sides. •In a rational function, after reducing, if a denominator exists, there is a SA if: -The numerator’s greatest exponent is exactly one more than the denominator’s greatest exponent. • To find the SA, do long division and ignore the remainder. Remember, it is a line so your answer should be in the form y=mx+b.