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Published byLeslie Purcell Modified over 3 years ago

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**Make sure you have book and working calculator EVERY day!!!**

Polynomial Functions 2.1 (M3)

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EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. Yes it’s a Polynomial. It is in standard form. Degree 4 – Quartic Trinomial Its leading coefficient is 1. a. h (x) = x4 – x2 + 3 1 4 b. Yes it’s a Polynomial. Standard form is Degree 2 – Quadratic Trinomial Leading Coefficient is

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EXAMPLE 1 Identify polynomial functions Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. c f (x) = 5x2 + 3x –1 – x c. Not a polynomial function d. k (x) = x + 2x – 0.6x5 d. Not a polynomial function e. f (x) = 13 – 2x e. polynomial function; f (x) = –2x + 13; degree 1 linear binomial, leading coefficient: –2

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**Graph Trend based on Degree**

Even degree - end behavior going the same direction Odd degree – end behavior (tails) going in opposite directions Leading Coefficient Leading Coefficient

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**Symmetry: Even/Odd/Neither**

First look at degree Even if it is symmetric respect to y-axis When you substitute -1 in for x, all signs stay the SAME Odd if it is symmetric with respect to the origin When you substitute -1 in for x, all of the signs CHANGE Neither if it is NOT symmetric around the y-axis or origin

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**Tell whether it is even/odd/neither**

f(x)= x2 + 2 f(x)= x2 - 4x f(x)= x3 f(x)= x3 + x f(x)= x3 + 5x +1

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**Additional Vocabulary to Review**

End Behavior: Left side x– ∞, f(x) ____ Right side x+∞, f(x) ____

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**Additional Vocabulary to Review**

Domain: set of all possible x values Range: set of all possible y values Symmetry: even (across y), odd (around origin), or neither Interval of increase (where graph goes up to the right) Interval of decrease (where the graph goes down to the right) End Behavior: Left side x– ∞, f(x) ____ Right side x+∞, f(x) ____

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**Polynomial Functions and Their Graphs**

There are several different elements to examine on the graphs of polynomial functions: Local minima and maxima:

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**Give the Local Maxima and Minima**

Must use y to describe High and Low On the graph above: A local maximum: f(x) = A local minimum: f(x) =

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**Finding a local max and/or local min is EASY with the calculator!**

Graph each of the following and find all local maxima or minima: Now describe their end behavior.

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**Describe the Interval of Increasing and Decreasing**

Must use x to describe Left to Right (Left to Right) The graph is: y x Increasing when ___________ Decreasing when _____________ Increasing when ___________

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**Assignment Page 69 #1-3 Classify #8-10 End Behavior**

#11-13 Symmetry (Even/Odd/Neither) #14-16 Max/Min, Domain/Range, Intervals of Increasing and Decreasing

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College Algebra 2.4 Properties of Functions Objectives: 1. Determine even or odd functions 2. Determine behavior of a function. 3. Find local min and max.

College Algebra 2.4 Properties of Functions Objectives: 1. Determine even or odd functions 2. Determine behavior of a function. 3. Find local min and max.

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