Exploring the Basics of Polynomials

The video tutorial reviews polynomials, focusing on end behavior. It explains the characteristics of polynomial graphs, such as continuity and smoothness, and how to classify them by degree. The tutorial discusses the impact of the leading coefficient on the end behavior of odd and even degree polynomials. It also covers notation for describing end behavior and provides examples to illustrate these concepts.

Which of the following is a characteristic of a polynomial graph?

• It has smooth, rounded corners.

• It is discontinuous.

• It has sharp corners.

• It has gaps.

What is the highest degree of a polynomial with the term x^5?

• 7

• 5

• 3

• 2

How do the ends of an odd degree polynomial behave?

• They end in the same direction.

• They both end down.

• They both end up.

• They end in different directions.

What happens to an even degree polynomial when the leading coefficient is positive?

• It has gaps.

• It ends in different directions.

• It opens upward.

• It opens downward.

If a polynomial has a negative leading coefficient and an odd degree, how does it behave?

• Ends up, starts up.

• Ends down, starts down.

• Ends down, starts up.

• Ends up, starts down.

What does the notation f(x) -> ∞ as x -> ∞ mean?

• As x increases, y decreases.

• As x decreases, y increases.

• As x increases, y increases.

• As x decreases, y decreases.

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In the case of an even degree polynomial with a negative leading coefficient, what is the end behavior?

• One end goes to negative infinity, the other to positive infinity.

• One end goes to positive infinity, the other to negative infinity.

• Both ends go to positive infinity.

• Both ends go to negative infinity.

For a polynomial with the highest degree of 5 and a positive leading coefficient, what is the end behavior?

• Ends up, starts down.

• Ends down, starts down.

• Ends down, starts up.

• Ends up, starts up.

What is the end behavior of a polynomial with the highest degree of 8 and a positive leading coefficient?

• Ends down, starts down.

• Ends down, starts up.

• Ends up, starts up.

• Ends up, starts down.

If a polynomial has a highest degree of 3 and a negative leading coefficient, what is its end behavior?

• Ends up, starts down.

• Ends down, starts up.

• Ends up, starts up.

• Ends down, starts down.