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# Precalc review

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### Transcript

• 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.