End Behavior Flashcardizz

Front

What is end behavior in polynomial functions?

Back

End behavior describes the behavior of the graph of a polynomial function as x approaches positive or negative infinity.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines the direction of the ends of the graph. Even degrees have both ends going in the same direction, while odd degrees have ends going in opposite directions.

Front

What does a positive leading coefficient indicate about the end behavior of a polynomial function?

Back

If the leading coefficient is positive and the degree is even, both ends of the graph will rise to positive infinity. If the degree is odd, the left end will fall to negative infinity and the right end will rise to positive infinity.

Front

What does a negative leading coefficient indicate about the end behavior of a polynomial function?

Back

If the leading coefficient is negative and the degree is even, both ends of the graph will fall to negative infinity. If the degree is odd, the left end will rise to positive infinity and the right end will fall to negative infinity.

Front

Given the polynomial f(x) = -2x^7 + 2x^4 + 4, what is its end behavior?

Back

As x → ∞, f(x) → -∞ and as x → -∞, f(x) → ∞.

Front

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

Back

The leading term of a polynomial function dominates the behavior of the function as x approaches infinity or negative infinity.

Front

How can you identify the degree of a polynomial?

Back

The degree of a polynomial is identified by the highest exponent of the variable in the polynomial.

Front

What is the end behavior of the polynomial f(x) = 3x^8 + 3x^5 - 4x + 7?

Back

As x → ∞, f(x) → ∞ and as x → -∞, f(x) → ∞.

Front

What does the notation x → ∞, y → ∞ mean?

Back

It means that as x increases without bound, the value of y also increases without bound.

Front

What does the notation x → -∞, y → -∞ mean?

Back

It means that as x decreases without bound, the value of y also decreases without bound.