1. Unit 2.1 – Evaluate and graph polynomial functions
Math 3 – Coach Bianco

2. Georgia performance standards
MM3A1b - Understand the effects of the following on the graph of a polynomial functions: degree, lead coefficient, and multiplicity of real zeros. MM3A1c – Determine whether a polynomial function has symmetry and whether it is even, odd, or neither. MM3A1d – Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

3. vocabulary A polynomial is a monomial or a sum of monomials.
The degree of a polynomial function is the exponent in the term where the variable is raised to the greatest power.
The leading coefficient is the coefficient in the term of a polynomial function that has the greatest exponent.
A polynomial function is in standard form if its terms are written in descending order of exponents from left to right.

4. vocabulary
Synthetic substitution is another way to evaluate a polynomial function, involving fewer operations than direct substitution.
The end behavior of a polynomial function’s graph is the behavior of the graph as x approaches infinity ( + ∞) or negative infinity ( - ∞).
End Behavior Rules:
positive coefficient, up on right end.
negative coefficient, down on right end.
even power, left end same as right end.
odd power, left end opposite from right end.

5. Review: Domain & range
Domain: Possible “x” values of a function Range: Possible “y” values of a function Hint: Think about the alphabet (D before R and X before Y)

6. Leading coefficient and degree
Put in standard form and identify the degree: 1.) -6x + 4x2 – 8x5 + x7 2.) 3x4-2x+7x4-3x8

7. Identify polynomial functions
Decide whether the function is a polynomial function. If so, write it in standard form and state its degree and leading coefficient. 1.) g(x) = -5x + 6x-2 2.) t(x) = − 𝟓𝒙 + 2

8. Answer
1.) The function g(x) is not a polynomial function because the term 6x-2 has an exponent that is not a whole number. 2.) the function t(x) is a polynomial function written in standard form. It has a degree 1 and a leading coefficient of − 𝟓𝒙

9. Direct substitution
g(x) = -4x3 + 3x2 – 7 when x = -2

10. Synthetic substitution
g(x) = -4x3 + 3x2 – 7 when x = -2

11. Describing end behavior

12. Graph and analyze a polynomial function
Graph and analyze the function f(x) = -2x4 + 4x2 -2.
Graph the function
Find the domain and range of the function
Describe the degree and leading coefficient of the function
Decide whether the function is even, odd, or neither.