Do Now: Evaluate the function for the given value of x. 1. f x   7x − 6; x  −2 2. g x   x 2  3; x  6 3. f x   −3x  4; x  −2 4. g x   x 2 − 6x ; x  − 4

Algebra II 4.1: Graphing Polynomial Functions Objective: To identify polynomials, and to use several techniques to get rough sketches.

Vocabulary What is a monomial? An expression that is either a number, a variable, or the product of a number and one or more variables

Vocabulary What is a Polynomial? A monomial or a sum of monomials

A polynomial function is in standard form when its terms are written in descending order of exponents from left to right.

Vocabulary Polynomial Function = a function in the form: n is the degree or the highest exponent. is the leading coefficient. is the constant term.

the exponents are all whole numbers What is a whole number? the coefficients are all real numbers What is a real number?

Common Polynomial Functions Degree Type Example Constant f(x)=-14 1 Linear f(x)=5x – 7 2 Quadratic f(x)=2x2+x-9 3 Cubic f(x)=x3-x2+3x 4 Quartic f(x)=x4+2x – 1

Think-Pair-Share: Write your own Degree Type Example 3 Constant Quartic f(x)=-x4+3x2+5 f(x)=-11x+24 Quadratic

Example 1

Decide whether the function is a polynomial function Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

Decide whether the function is a polynomial function Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.

Example 2 Evaluate f (x ) = 2x 4 − 8x 2 + 5x − 7 when x = 3.

Closing Exit Ticket: State the degree, type, and leading coefficient of the following function, then an example of a polynomial with those same characteristics. f (x ) = 3.5x 4 + 4x 2 − 7x + 2

Homework: Textbook page 162 # 4-16 evens