5.3 Polynomial Functions By Willis Tang.

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Presentation transcript:

5.3 Polynomial Functions By Willis Tang

Major Topics Describing end behaviors of polynomial functions Finding real zeroes Identifying degree and leading polynomials

The degree would be 3 and the leading coefficient would be 4. Terms Leading coefficient:The coefficient of the first term of the polynomial in standard form Polynomial Function: continuous function that can be described by a polynomial equation in one variable Polynomial equation in one variable: A polynomial equation with one variable Degree: Highest exponent Ex: 4x3+2x2+3x+5 The degree would be 3 and the leading coefficient would be 4.

Example 1: Describe the end behavior Determine whether it represents an odd- degree or an even- degree polynomial function State the number of real zeroes Answer: f(x) +∞ as x -∞, f(x) +∞ as x + ∞ Even-degree function 4 real zeroes

Example 2: Describe the end behavior Determine whether it represents an odd- degree or an even- degree polynomial function State the number of real zeroes Answer: f(x) -∞ as x -∞, f(x) +∞ as x + ∞ Odd-degree function 5 real zeroes

Find the leading coefficient and degree Example 3: Find the leading coefficient and degree 3x4+8x3+2x2+9x+5 Answer: Leading Coefficient: 3 Degree: 4

Practice Problem #1 Describe the end behavior Determine whether it represents an odd- degree or an even- degree polynomial function State the number of real zeroes Answer: f(x) +∞ as x -∞, f(x) -∞ as x + ∞ Odd-degree function 3 real zeroes

Practice Problem #2 Describe the end behavior Determine whether it represents an odd- degree or an even- degree polynomial function State the number of real zeroes Answer: f(x) +∞ as x -∞, f(x) +∞ as x + ∞ Even-degree function 4 real zeroes ( one double root )

Find the leading coefficient and degree Practice Problem #3 Find the leading coefficient and degree 5x5+6x4+x3+9x2+4x+10 Answer: Leading Coefficient: 5 Degree: 5