Exploring End Behavior in Polynomial Functions

The video tutorial covers polynomial functions and their end behavior, focusing on how to describe the behavior of functions as they approach positive and negative infinity. It introduces limit notation to express these behaviors and explains the impact of the leading term's degree and coefficient on the function's end behavior. The tutorial distinguishes between even and odd degree polynomials, providing examples and practice problems to reinforce the concepts.

What happens to a polynomial function as x approaches negative infinity?

• It remains undefined.

• It oscillates.

• It goes up or down.

• It becomes constant.

Which notation is used to describe the end behavior of a function as x approaches negative infinity?

• lim x → ∞

• lim x → -∞

• lim y → -∞

• lim y → ∞

If a function increases as x approaches negative infinity, how is it described using limit notation?

• lim x → -∞ P(x) = ∞

• lim x → -∞ P(x) = -∞

• lim x → ∞ P(x) = ∞

• lim x → ∞ P(x) = -∞

What is the end behavior of a polynomial function if it decreases as x approaches positive infinity?

• lim x → ∞ P(x) = ∞

• lim x → -∞ P(x) = ∞

• lim x → ∞ P(x) = -∞

• lim x → -∞ P(x) = -∞

How do you determine the end behavior of a polynomial function without looking at the graph?

• By checking the constant term.

• By evaluating the middle terms.

• By analyzing the leading term.

• By considering the y-intercept.

What happens to the end behavior of a polynomial function if the leading term has an even degree and a positive coefficient?

• Both ends go up.

• Both ends go down.

• One end goes up, the other goes down.

• It remains constant.

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

• Both ends go up.

• Both ends go down.

• Left end goes down, right end goes up.

• Left end goes up, right end goes down.

If a polynomial function has a leading term with an odd degree and a negative coefficient, what is the end behavior?

• Left end goes up, right end goes down.

• Both ends go up.

• Left end goes down, right end goes up.

• Both ends go down.

What is the end behavior of the function P(x) = -x^3 as x approaches negative infinity?

• lim x → -∞ P(x) = -∞

• lim x → ∞ P(x) = ∞

• lim x → ∞ P(x) = -∞

• lim x → -∞ P(x) = ∞

What is the end behavior of the function P(x) = x^2 as x approaches positive infinity?

• lim x → ∞ P(x) = ∞

• lim x → ∞ P(x) = -∞

• lim x → -∞ P(x) = ∞

• lim x → -∞ P(x) = -∞