Describe the end behavior of the function $$f(x) = 4x^{10}$$ .

As $$x \to -\text{infinity}$$ , $$f(x) \to +\text{infinity}$$ and as $$x \to +\text{infinity}$$ , $$f(x) \to +\text{infinity}$$ .

What is the end behavior of $$g(x) = -2x^6 + 2x^5 - 12x - 6$$ ?

As $$x \to -\text{infinity}$$ , $$g(x) \to -\text{infinity}$$ and as $$x \to +\text{infinity}$$ , $$g(x) \to -\text{infinity}$$ .

What is the end behavior of a polynomial function with a leading coefficient less than zero and an even degree?

As $$x \to -\text{infinity}$$ , the function approaches $$-\text{infinity}$$ and as $$x \to +\text{infinity}$$ , the function also approaches $$-\text{infinity}$$ .

What is the end behavior of a polynomial function with a leading coefficient less than zero and an odd degree?

As $$x \to -\text{infinity}$$ , the function approaches $$+\text{infinity}$$ and as $$x \to +\text{infinity}$$ , the function approaches $$-\text{infinity}$$ .

What is the significance of the leading term in determining end behavior?

The leading term of a polynomial determines the end behavior of the function as it dominates the polynomial for large values of $$|x|$$ .

What is the end behavior notation for a function that approaches infinity as x approaches infinity?

The notation is: $$\text{as } x \to \text{infinity}, f(x) \to \text{infinity}$$ .

What is the end behavior notation for a function that approaches negative infinity as x approaches infinity?

The notation is: $$\text{as } x \to \text{infinity}, f(x) \to -\text{infinity}$$ .

How can you determine the end behavior of a polynomial function from its graph?

You can determine the end behavior by observing the direction in which the graph heads as $$x$$ approaches positive and negative infinity.

What is the relationship between the degree of a polynomial and the number of turning points?

A polynomial of degree $$n$$ can have at most $$n-1$$ turning points.

End Behavior Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

2.

FLASHCARD QUESTION

Front

Back

4

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What does it mean when a polynomial has an odd degree?

Back

If a polynomial has an odd degree, its end behavior will be opposite on either side: one side will go to positive infinity and the other to negative infinity.

6.

FLASHCARD QUESTION

Front

What does it mean when a polynomial has an even degree?

Back

If a polynomial has an even degree, its end behavior will be the same on both sides: both sides will either go to positive infinity or negative infinity.

7.

FLASHCARD QUESTION

Front

What is the end behavior of a polynomial function with a leading coefficient greater than zero and an even degree?

Back

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