Analyzing Polynomial End Behavior and Zeros

The video tutorial explains how to determine the end behavior of polynomial functions using the leading coefficient test and graph analysis. It covers how to estimate the zeros of a polynomial and determine whether the polynomial is of even or odd degree based on the number of zeros. The tutorial emphasizes understanding the graph's behavior as x approaches positive and negative infinity.

What is the first step in determining the end behavior of a polynomial?

• Identifying the x-intercepts

• Using the leading coefficient test

• Calculating the derivative

• Finding the y-intercepts

What does the leading coefficient test help you determine?

• The degree of the polynomial

• The y-intercepts

• The number of zeros

• The end behavior of the polynomial

As x approaches positive infinity, what happens to the f(x) values in the given example?

• They approach positive infinity

• They approach zero

• They remain constant

• They approach negative infinity

Tags

CCSS.HSF-IF.C.7E

What is the end behavior of the polynomial as x approaches negative infinity?

• f(x) approaches positive infinity

• f(x) remains constant

• f(x) approaches zero

• f(x) approaches negative infinity

How many zeros does the polynomial have in the given example?

• Two

• None

• Three

• One

What are the zeros of a polynomial also known as?

• Asymptotes

• Turning points

• Y-intercepts

• X-intercepts

Tags

CCSS.HSF-IF.C.7C

If a polynomial has two zeros, what can be inferred about its degree?

• It is a linear polynomial

• It has no degree

• It is an even degree polynomial

• It is an odd degree polynomial

Tags

CCSS.HSF-IF.C.7C

What is true about the number of zeros in an even degree polynomial?

• It always has exactly one zero

• It has no zeros

• It always has an odd number of zeros

• It always has an even number of zeros or none

What is the end behavior of the polynomial as x approaches positive infinity?

• f(x) remains constant

• f(x) approaches negative infinity

• f(x) approaches zero

• f(x) approaches positive infinity

What is the end behavior of the polynomial as x approaches negative infinity?

• f(x) approaches zero

• f(x) approaches negative infinity

• f(x) remains constant

• f(x) approaches positive infinity