SOLVING RATIONAL RATIONAL FUNCTIONS.pptx

Mathematics 9

1. RATIONAL FUNCTIONS, EQUATIONS, AND INEQUALITIES

2. POLYNOMIAL FUNCTION p of degree n is a function that can be written in the form , where , ,…, , and is a positive integer. Each addend of the sum is term of the polynomial function. The constant , ,…, are the coefficients . The leading coefficient is . The leading term is , and the constant term is .  

3. Example: Given the polynomial function , find The degree of polynomial The leading coefficient The constant term The number of zeroes     3 IS THE DEGREE OF POLYNOMIAL (highest degree of the function) -1 IS THE LEADING COEFFICIENT (coefficient of the term with the highest degree of the function) CONSTANT THERE ARE 3 ZEROES OF THE FUNCTION (the number of zeroes is the same as the highest degree of the fucntion )

4. RATIONAL EXPRESSION an expression that can be written as a ratio of two polynomials ( polynomials is an expression consisting of variables and coefficients with one or more term and variables, examples— ) C onditions when an expression is considered as a polynomial: n o negative exponent (Ex. ) no radicals (Ex. ) no fraction as exponent (Ex. ) Therefore, if an expression (whether the numerator/ denominator) is not a polynomial, then it is not a rational expression.  

5. RATIONAL EQUATION an equation involving rational equations and uses symbol RATIONAL INEQUALITY a rational expression combines with any of these inequality symbols: RATIONAL INEQUALITY a function of the form where and are polynomial functions and is not the zero function (i.e., ). The domain of is the set of all values of where .  

6. RATIONAL EQUATION Solve for : 1.  

7. 2.  

8. 3.  

9. Solve for : 3.    

10. SEATWORK: Solve for . 1.  

11. SEATWORK: Solve for . 2 .  

12. RATIONAL INEQUALITY Solve for : 1.   ↓   Testing  

13. Testing -1   Testing positive number: 3   Testing negative number: -2   Testing 0   X X

14. 2.   ↓   Testing   X

15. Testing positive number: 2   Testing negative number: -2   Testing 0   X Testing 1   X

16. RATIONAL FUNCTION Solve for : 1.