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Understanding Polynomial Functions: Degree, End Behavior, and Key Characteristics

This guide explores essential concepts of polynomial functions, focusing on their degree, end behavior, number of zeros, and turning points. Learn how to determine the zeros of a polynomial, analyze its behavior at those zeros, find the y-intercept, and evaluate additional significant points on the graph. The end behavior of a polynomial function describes how the graph behaves as x approaches infinity or negative infinity. Through illustrative examples, we will solidify your understanding of polynomial behavior and guide you to graphing polynomials accurately.

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Understanding Polynomial Functions: Degree, End Behavior, and Key Characteristics

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  1. Graphing Polynomials • Determine degree • End behavior • Number of Zeros • Turning points • Find the zeros and determine behavior at zero • Find the y-intercept and a few other points

  2. The end behavior of a polynomial function’s graph is the behavior of the graph as x approaches infinity (+ ) or negative infinity (– ). The expression x+ is read as “x approaches positive infinity.” END BEHAVIOR

  3. What we already know • Think about the end behavior of the following

  4. Let’s Explore • Consider the following functions. • Degree 3 • Leading Coefficient 1 • Degree 3 • Leading Coefficient -2

  5. Let’s Explore • Consider the following functions. • Degree 4 • Leading Coefficient -3 • Degree 4 • Leading Coefficient1

  6. CONCEPT END BEHAVIOR FOR POLYNOMIAL FUNCTIONS SUMMARY LCdegx – x + > 0 even f(x) + f(x) +  > 0 odd f(x) – f(x) +  < 0 even f(x) – f(x) –  < 0 odd f(x) + f(x) –  END BEHAVIOR

  7. HOMEWORK 11/15 PAGE 354-356, 1-18 all,

  8. MULTIPLICITY x+3 is a factor of this polynomials. Graph the polynomial.

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