End Behavior of Polynomials: Leading Coefficient Test Insights

This video tutorial explains how to determine the end behavior of polynomial graphs. It covers the influence of the leading coefficient and degree on the graph's direction, both to the right and left. The video also introduces notation used to describe end behavior, including limit notation. Several examples are provided to illustrate these concepts, and viewers are encouraged to practice on their own.

What is the primary focus when determining the end behavior of a polynomial?

• The constant term

• The leading coefficient

• The middle term

• The lowest power term

If the leading coefficient of a polynomial is positive, what can be said about the graph's behavior to the right?

• It goes down

• It goes up

• It stays constant

• It oscillates

How does an odd degree polynomial behave on the left end compared to the right end?

• It oscillates

• It goes in the same direction

• It goes in the opposite direction

• It stays constant

What does the notation 'as X approaches Infinity, f(x) approaches Infinity' signify?

• The graph goes down to the right

• The graph goes up to the right

• The graph goes down to the left

• The graph stays constant

In limit notation, what does 'limit as X approaches negative Infinity, f(x) approaches negative Infinity' mean?

• The graph goes down to the left

• The graph goes up to the right

• The graph goes down to the right

• The graph goes up to the left

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

• Up to the right, up to the left

• Down to the right, up to the left

• Down to the right, down to the left

• Up to the right, down to the left

What is the end behavior of the polynomial f(x) = x^8 - 2x^5 + 4?

• Down to the right, down to the left

• Up to the right, up to the left

• Down to the right, up to the left

• Up to the right, down to the left

For the polynomial f(x) = -10x^7 - 3x^2 + 5, what is the end behavior?

• Down to the right, down to the left

• Up to the right, down to the left

• Down to the right, up to the left

• Up to the right, up to the left

What is the end behavior of the polynomial f(x) = -1/2 x^6 + x^3 - 2?

• Down to the right, down to the left

• Up to the right, up to the left

• Down to the right, up to the left

• Up to the right, down to the left

For the polynomial f(x) = 8x^5 - 2x^4 + 3x^2 + 1, what is the end behavior?

• Up to the right, up to the left

• Up to the right, down to the left

• Down to the right, down to the left

• Down to the right, up to the left