End Behavior

Front

What is end behavior in the context of polynomial functions?

Back

End behavior describes how the values of a polynomial function behave as the input (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 the same end behavior, while odd degrees have opposite end behavior.

Front

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

Back

The sign of the leading coefficient (positive or negative) influences whether the ends of the graph rise or fall as x approaches infinity.

Front

If a polynomial has an even degree and a positive leading coefficient, what is its end behavior?

Back

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

Front

If a polynomial has an odd degree and a negative leading coefficient, what is its end behavior?

Back

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

Front

What does it mean if a polynomial's end behavior is described as both ends going to -∞?

Back

This indicates that as x approaches both positive and negative infinity, the function values decrease without bound.

Front

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

Back

By observing the direction in which the graph extends as x approaches positive and negative infinity.

Front

What is the end behavior of the polynomial f(x) = -2x^4 + 3x^3 - x + 5?

Back

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

Front

What is the end behavior of the polynomial f(x) = x^3 - 4x + 1?

Back

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

Front

If a polynomial has a degree of 4, what can you infer about its end behavior?

Back

It will have the same end behavior on both sides, either both going to +∞ or both going to -∞.