Exploring End Behavior of Polynomial Functions

The video tutorial explains the behavior of polynomial graphs based on the leading coefficient and degree. It covers how the leading coefficient determines the right end behavior, with positive coefficients causing the graph to rise and negative coefficients causing it to fall. The degree of the polynomial affects the left end behavior, with even degrees resulting in the same direction as the right end and odd degrees resulting in the opposite direction. Examples are provided to illustrate these concepts.

What are the four possible behaviors of a polynomial graph?

• Up to the right, down to the right, up to the left, down to the left

• Up to the right, up to the left, down to the right, down to the left

• Up to the right, down to the right, up to the left, up to the right

• Down to the right, down to the left, up to the right, up to the left

What determines whether a polynomial graph goes up or down to the right?

• The leading coefficient

• The y-intercept

• The second highest degree term

• The constant term

If the leading coefficient of a polynomial is positive, what is the right end behavior?

• Goes up to the left

• Goes down to the right

• Goes down to the left

• Goes up to the right

Why can we ignore lower degree terms when determining the end behavior of a polynomial?

• They grow faster than the highest degree term

• They grow slower than the highest degree term

• They have no impact on the graph

• They are always zero

What does the degree of a polynomial tell us about its left end behavior?

• It only affects the right end behavior

• It has no impact on the left end behavior

• If it is odd, the behavior is the same; if even, it is opposite

• If it is even, the behavior is the same; if odd, it is opposite

For the polynomial y = 2x^3, what is the left end behavior?

• Goes up to the left

• Goes down to the right

• Goes down to the left

• Goes up to the right

For the polynomial y = -2x^3, what is the right end behavior?

• Goes up to the left

• Goes down to the left

• Goes down to the right

• Goes up to the right

For the polynomial y = 2x^4, what is the end behavior on both sides?

• Goes up to the right and down to the left

• Goes down to the right and up to the left

• Goes down to the right and down to the left

• Goes up to the right and up to the left

For the polynomial y = -2x^4, what is the end behavior on both sides?

• Goes up to the right and down to the left

• Goes down to the right and up to the left

• Goes up to the right and up to the left

• Goes down to the right and down to the left

What is the behavior of the polynomial y = 2x^3 as x approaches negative infinity?

• Goes down to the right

• Goes down to the left

• Goes up to the left

• Goes up to the right