Do Now: Match each polynomial function with its graph. Explain your reasoning. Use a graphing calculator to verify your answers. 1. f (x) = x 3 − x 2. f (x) = −x 3 + x 3. f (x) = −x f (x) = x 4 5. f (x) = x 3 6. f (x) = x 4 − x 2

4.1: GRAPHING POLYNOMIAL FUNCTIONS DAY 1 Objective: identify and evaluate polynomial functions Homework: p162, #4-8, all evens

What are some common characteristics of the graphs of cubic and quartic polynomial functions?

Vocabulary Polynomial: Examples: Polynomial function: Example: If you can answer yes to any of these, it is not a polynomial function:

Vocabulary Leading coefficient: Degree: Constant term: Write in standard form: f(x) = – 2x 3 – 8 – 5x 4 - x 2

Identify the following: DegreeTypeLeading Coefficient

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

Practice Decide whether each function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. 4. f(x) = −4x 5 + 7x 2 − 2

f(x) = −2x 4 + 6x 3 − 3x + 11; when x = 4 f(x) = 2x 4 − 8x 2 + 5x − 7; when x = 3 Evaluate

Practice Evaluate f(x) = −x 3 + 3x 2 + 9; when x = 4 f(x) = 3x 5 − x 4 − 6x + 10; when x = −2

Closure Describe what the following are in your own words: A. Leading coefficient B. Degree C. Constant

Do Now: Student Journal p79 #1-2, 5

4.1: GRAPHING POLYNOMIAL FUNCTIONS DAY 2 Objective: identify and evaluate polynomial functions and describe end behaviors of graphs Homework: p162, #17-22

Vocabulary End behavior:

Describing End Behaviors End Behaviors of a polynomial with an even degree: End Behaviors of a polynomial with an odd degree: Positive leading coefficient: Negative leading coefficient: Positive leading coefficient: Negative leading coefficient:

Describe the end behavior of the graph of: f(x) = −0.5x x 2 + x − 1 f(x) = 0.25x 3 − x 2 − 1

Practice Describe the end behavior of the graph of: p(x) = 3 − x 4 f(x) = 4x − 9 − x 3 g(x) = x 3 + x + 3 p(x) = x 5 − 3x 3 + 2

Do Now: Student Journal p79 Describe the end behavior.

4.1: GRAPHING POLYNOMIAL FUNCTIONS DAY 3 Objective: identify and evaluate polynomial functions, describe end behaviors of graphs Homework: 4.1 Practice Worksheet A