1. Friday February 7, 2014 5.1 Properties of Exponent Objective: To evaluate or simplify expression with powers EQ: Can you multiply and divide negative fraction powers? Example 1: Evaluate the following expression Solution: Example 1: Evaluate the following expression Solution:

2. Friday February 7, 2014 5.1 Properties of Exponent Example 2: Solution: Example 2: Solution: Example 3: Simplify the followings Solution: Example 3: Simplify the followings Solution: Example 4: Simplify the followings Solution: Example 4: Simplify the followings Solution:

3. A polynomial function has the standard form: where all the terms are written in descending order of exponents from left to right a n is leading coefficient, real number a 0 is constant term, real number n is the degree (exponent), whole number A polynomial function has the standard form: where all the terms are written in descending order of exponents from left to right a n is leading coefficient, real number a 0 is constant term, real number n is the degree (exponent), whole number 5.2 Polynomials Functions Objective: To evaluate and graph any polynomial function EQ: Can you identify a polynomial function just by its graph? Example 1: Decide whether the function is a polynomial function then write it in standard form and identify the degree, type and leading coefficient a. Yes, already in standard form, degree is 4, type is quartic, leading coefficient is 1 b. Yes, standard form is,degree is 2, type quadratic, leading coefficient is π Example 1: Decide whether the function is a polynomial function then write it in standard form and identify the degree, type and leading coefficient a. Yes, already in standard form, degree is 4, type is quartic, leading coefficient is 1 b. Yes, standard form is,degree is 2, type quadratic, leading coefficient is π Example 1: Friday February 7, 2014

4. Tuesday February 11, 2014 5.2 Polynomials Functions Example 1: Decide whether the function is a polynomial function then write it in standard form and identify the degree, type and leading coefficient c. No, because x -1 is not whole number d. No, 2 x is not a variable base Example 1: Decide whether the function is a polynomial function then write it in standard form and identify the degree, type and leading coefficient c. No, because x -1 is not whole number d. No, 2 x is not a variable base Evaluate by direct substitution Evaluate by synthetic division Evaluate by synthetic division

5. End Behavior of a function’s graph: is the behavior of the graph as x approaches ±∞. The behavior is determined by the polynomial’s degree and leading coefficient sign. Wednesday February 12, 2014 5.2 Polynomials Functions Example : Determine the end behavior of the following polynomials a.f(x) = -x 3 + x 2 + 3x – 3b. g(x) = x 4 - x 3 - 4x 2 + 4 Example: Describe the degree and leading coefficient (LC)? Degree: even, LC: negative Degree: odd, LC: positive Example : Determine the end behavior of the following polynomials a.f(x) = -x 3 + x 2 + 3x – 3b. g(x) = x 4 - x 3 - 4x 2 + 4 Example: Describe the degree and leading coefficient (LC)? Degree: even, LC: negative Degree: odd, LC: positive

6. Wednesday February 12, 2014 5.2 Polynomials Functions