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# Polynomial Functions - PowerPoint PPT Presentation

Polynomial Functions. Lesson 9.2. Polynomials. Definition: The sum of one or more power function Each power is a non negative integer. Polynomials. General formula a 0 , a 1 , … ,a n are constant coefficients n is the degree of the polynomial

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## PowerPoint Slideshow about 'Polynomial Functions' - maximos

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### Polynomial Functions

Lesson 9.2

• Definition:

• The sum of one or more power function

• Each power is a non negative integer

• General formula

• a0, a1, … ,an are constant coefficients

• n is the degree of the polynomial

• Standard form is for descending powers of x

• anxn is said to be the “leading term”

• Consider what happens when x gets very large negative or positive

• Called “end behavior”

• Also “long-run” behavior

• Basically the leading term anxn takes over

• Comparef(x) = x3 with g(x) = x3 + x2

• Look at tables

• Use standard zoom, then zoom out

• Compare tables for low, high values

The leading term x3 takes over

For 0 < x < 500the graphs are essentially the same

Polynomial Properties

• Compare graphs ( -10 < x < 10)

• We seek values of x for which p(x) = 0

• Consider

• What is the end behavior?

• What is q(0) = ?

• How does this tell us that we can expect at least two roots?

• Graph and ask for x-axis intercepts

• Use solve(y1(x)=0,x)

• Use zeros(y1(x))

• When complex roots exist, use cSolve() or cZeros()

• Giveny = (x + 4)(2x – 3)(5 – x)

• What is the degree?

• How many terms does it have?

• What is the long run behavior?

• f(x) = x3 +x + 1 is invertible (has an inverse)

• How can you tell?

• Find f(0.5) and f -1(0.5)

• Lesson 9.2

• Page 400

• Exercises 1 – 29 odd