End Behavior of Polynomials

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the values of the polynomial function behave as the input (x) approaches positive or negative infinity.

Front

What does y → ∞ indicate?

Back

It indicates that the value of y is increasing without bound as x approaches a certain value.

Front

What does y → -∞ indicate?

Back

It indicates that the value of y is decreasing without bound as x approaches a certain value.

Front

How do you determine the end behavior of a polynomial function?

Back

To determine the end behavior, analyze the leading term of the polynomial and its degree, as well as the sign of the leading coefficient.

Front

What is the end behavior of f(x) = x^3?

Back

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

Front

What is the end behavior of f(x) = -x^3?

Back

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

Front

What is the end behavior of f(x) = x^2?

Back

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

Front

What is the end behavior of f(x) = -x^2?

Back

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

Front

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

Back

If a polynomial has an even degree, its end behavior will be the same in both directions (either both up or both down).

Front

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

Back

If a polynomial has an odd degree, its end behavior will be opposite in each direction (one direction goes up, the other goes down).