Polynomial
• An expression or equation that is the sum of monomials •An expression or equation having many (poly) terms
Rational Function
• A function that is the ratio or division of two polynomials
Asymptotes
• Lines that graphs  approach,  but never touch
Vertical Asymptote (VA)
• Vertical line(s) that graphs  approach,  but never touch • After you factor a rat’l function and reduce, VA’s come from ...
Holes
• Point(s) in graphs that are undefined. • After you factor a rat’l function and reduce, holes come from factors in the de...
Horizontal Asymptote (HA)
• HA’s are line(s) that graphs  approach,  but never touch • These lines show the end behavior of graphs on the left and r...
Slant Asymptote (SA) of Oblique Asymptotes
• Slant line(s) that graphs  approach,  but never touch • These lines show the end behavior of graphs on the left and righ...
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Precalc review

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Precalc review

  1. 1. Polynomial
  2. 2. • An expression or equation that is the sum of monomials •An expression or equation having many (poly) terms
  3. 3. Rational Function
  4. 4. • A function that is the ratio or division of two polynomials
  5. 5. Asymptotes
  6. 6. • Lines that graphs approach, but never touch
  7. 7. Vertical Asymptote (VA)
  8. 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. 9. Holes
  10. 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. 11. Horizontal Asymptote (HA)
  12. 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. 13. Slant Asymptote (SA) of Oblique Asymptotes
  14. 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.

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