Math 3 Lesson 2.1,2.2, and 2.3 EVALUATE AND GRAPH POLYNOMIAL FUNCTIONS - TRANSLATE GRAPHS OF POLYNOMIAL FUNCTIONS Unit 2: Polynomial Functions Standards: MA3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions as translations of the function. b. Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros. c. Determine whether a polynomial function has symmetry and whether it is even, odd, or neither. d. 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.

Polynomial: Degree: Leading Coefficient: Vocabulary

(Ex 1) Decide whether the function is a polynomial function. If so, write it in standard form and state its degree and leading coefficient. a) g(x)=-5x+6x -2 b) f(x)=2x-5x 2 -3

To Graph: 1. Find X-intercepts (Solve equation for zeros) 2. Determine Degree (Odd or Even) –most # of zeros 3. Determine Leading Coefficient (Positive or Negative) 4. Determine # of Turning Points (Degree minus 1) 5. Make a table ………………………………………………………………….. Odd/Pos Odd/Neg Even/Pos Even/Neg

G RAPHING P OLYNOMIAL F UNCTIONS END BEHAVIOR FOR POLYNOMIAL FUNCTIONS C ONCEPT S UMMARY > 0even f (x)+  f (x) +  > 0odd f (x)–  f (x) +  < 0even f (x)–  f (x) –  < 0odd f (x)+  f (x) –  a n n x –  x + 

EX.EX. Determine the left and right behavior of the graph of each polynomial function. f(x) = -x 5 +3x 4 – x f(x) = x 4 + 2x 2 – 3x f(x) = 2x 3 – 3x 2 + 5

T ELL ME WHAT YOU KNOW ABOUT THE EQUATION … Odd exponent Positive leading coefficient

T ELL ME WHAT YOU KNOW ABOUT THE EQUATION … Even exponent Positive leading coefficient

T ELL ME WHAT YOU KNOW ABOUT THE EQUATION … Odd exponent Positive leading coefficient

T ELL ME WHAT YOU KNOW ABOUT THE EQUATION … Even exponent Negative leading coefficient

Domain: Range: Even: Odd: Intervals of increase: Intervals of decrease: End behavior: Analyzing a Graph:

(Ex. 4) Graph and analyze the function f(x) = -2x 4 +4x 2 -2 a) Domain: b) Range: c) Even, Odd or Neither d) Increasing: e) Decreasing: f) Describe the end behavior: f(x)  _____ as x  _____

(Ex. 5) Graph and analyze the function f(x) = x 3 -x 2 -2x a) Domain: b) Range: c) Even, Odd or Neither d) Increasing: e) Decreasing: f) Describe the end behavior: f(x)  _____ as x  _____

Standard FormParent Graph f(x)=a(x-h) 2 +kf(x)=x 2 f(x)=a(x-h) 3 +kf(x)=x 3 f(x)=a|x-h|+kf(x)=|x| Negative “a” – Negative in front of “x” – |a|<1 – |a|>1 – h – k – Parent Functions:

f(x) = x 3 f(x) = x 2 f(x) = |x| Parent Functions:

(Ex. 6) Graph: a) f(x) = x 2 b) f(x) = -x 2 c) f(x) = x 2 +2

(Ex. 7) Graph: a) f(x) = |x| b) f(x) = |x| -1 c) f(x) = 3|x-3|

(Ex. 8) Identify the common function. Write the transformation shown in the graph. Write the formula for the graphed function. a)b)

(Ex.9) Compare the graph of the function with the parent graph.

Assignment: Math 3 Book: p. 70 # 5 -7 (all); # (all) p. 74 # 1- 3(all); 5 – 19 (odd)