Determining End Behavior of Polynomials

The video tutorial explains how to identify the end behavior of polynomials using the leading coefficient test. It covers the importance of ensuring polynomials are in descending order and differentiates between powers and coefficients. Through examples, the tutorial demonstrates how to determine the degree and leading coefficient, and how these affect the end behavior of the graph. The video also emphasizes the use of interval notation to describe end behavior.

What is the first step in using the leading coefficient test?

• Ensure the function is a polynomial

• Identify the degree of the polynomial

• Arrange terms in ascending order

• Find the leading coefficient

What must be true about the exponents in a polynomial function?

• They can be negative

• They must be even numbers

• They must be non-negative integers

• They can be fractions

How should the terms of a polynomial be arranged?

• In ascending order of coefficients

• In descending order of powers

• In random order

• In ascending order of powers

What is the degree of the polynomial 5x^4 - 3x^2 + 2x?

• 4

• 5

• 3

• 2

If a polynomial has an even degree and a positive leading coefficient, what is the end behavior?

• Falls left, rises right

• Rises left, rises right

• Falls left, falls right

• Rises left, falls right

What is the leading coefficient of the polynomial 5x^4 - 3x^2 + 2x?

• 5

• 4

• 3

• 2

For a polynomial with an odd degree and a negative leading coefficient, what is the end behavior?

• Rises left, rises right

• Rises left, falls right

• Falls left, falls right

• Falls left, rises right

What is the degree of the polynomial 4x^9 + 2x^8 + 5?

• 5

• 4

• 9

• 8

If a polynomial has an odd degree and a positive leading coefficient, what is the end behavior?

• Rises left, rises right

• Falls left, rises right

• Rises left, falls right

• Falls left, falls right

What is the leading coefficient of the polynomial x^4 + 5?

• 5

• 1

• 4

• -1