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Rational functions, equations, inequalities.pptx
- 2. POLYNOMIAL an expression consisting of variables (such as x and y) and coefficients with one or more than one term and variables Examples: 𝟏, 𝒙𝟑 , 𝟑𝒙𝟐 − 𝒙 + 𝟏 and 𝒙𝟑 + 𝟐𝒙𝒚𝒛𝟐 − 𝒚𝒛 + 𝟏 an expression that can be written as a ratio of two polynomials
- 3. The variable of any term has a negative exponent. CONDITIONS WHERE AN EXPRESSION IS NOT CONSIDERE D AS A POLYNOMIA L: 4𝑥−3 + 2𝑥2 − 5
- 4. The variable of any term is inside the radical symbol. CONDITIONS WHERE AN EXPRESSION IS NOT CONSIDERE D AS A POLYNOMIA L: 4𝑥2 − 𝑥
- 5. The variable of any term has a fraction as exponent. CONDITIONS WHERE AN EXPRESSION IS NOT CONSIDERE D AS A POLYNOMIA L: 𝑥 2 3 + 3𝑥 − 1
- 6. Therefore, if an expression (whether the numerator or denominator) is not a polynomial, then it is not a RATIONAL EXPRESSION. 4𝑥−3 + 2𝑥2 − 5 4𝑥2 − 𝑥 𝑥 2 3 + 3𝑥 − 1
- 7. an equation involving rational expression only uses = symbol (equal sign) a rational expression combines with any of these inequality symbols <, >, ≤, or ≥ a function of the form 𝒇 𝒙 = 𝒑(𝒙) 𝒒(𝒙) , where 𝒑(𝒙) and 𝒒 𝒙 are polynomial functions , and 𝒒(𝒙) is not a zero function The domain of 𝒇(𝒙) is all values of 𝒙 where 𝒒(𝒙) ≠ 𝟎 RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION
- 8. 𝟑 𝒙 − 𝟐 𝟑𝒙 = 𝟏 𝒙 𝒙𝟑 + 𝟑𝒙 − 𝟐 𝒙 = 𝟑 𝒙 𝒙 − 𝟐 𝟒𝒙 < 𝟓 𝟒 𝒙𝟐 − 𝟑𝒙 + 𝟒 ≥ 𝟑 𝒙 𝒇 𝒙 = 𝒙𝟐 − 𝟐𝒙 − 𝟑 𝒙 + 𝟐 or 𝒚 = 𝒙𝟐 − 𝟐𝒙 − 𝟑 𝒙 + 𝟐 RATIONAL EQUATION RATIONAL INEQUALITY RATIONAL FUNCTION