How to write informally the end behavior of the leading coefficient test

The video tutorial explains the end behavior of polynomial graphs based on their degree and leading coefficient. For even degree polynomials with a positive leading coefficient, the graph rises to both the left and right. For odd degree polynomials with a positive leading coefficient, the graph falls to the left and rises to the right. An example using a fifth-degree polynomial is provided to illustrate these concepts.

What is the end behavior of an even-degree polynomial with a positive leading coefficient?

• Rises to the left and falls to the right

• Falls to the left and rises to the right

• Falls to both the left and right

• Rises to both the left and right

For an odd-degree polynomial with a positive leading coefficient, how does the graph behave as it moves to the left?

• It oscillates

• It remains constant

• It falls

• It rises

How does the graph of an odd-degree polynomial with a positive leading coefficient behave as it moves to the right?

• It oscillates

• It remains constant

• It rises

• It falls

In the example of the polynomial F(x) = 3x^5 - 7, what is the end behavior of the graph?

• Rises to the left and falls to the right

• Falls to the left and rises to the right

• Rises to both the left and right

• Falls to both the left and right

What is the significance of the leading coefficient in determining the end behavior of a polynomial?

• It has no effect on the graph's behavior

• It determines the degree of the polynomial

• It affects the graph's symmetry

• It influences whether the graph rises or falls