Polynomial Functions

1 / 10

# 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Polynomial Functions' - maximos

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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
• 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”
Polynomial Properties
• 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
Polynomial Properties
• 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)
Zeros of Polynomials
• 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?
Methods for Finding Zeros
• 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()
Practice
• 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)
Assignment
• Lesson 9.2
• Page 400
• Exercises 1 – 29 odd