End Behavior of Polynomials

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an even degree?

Back

As x → ±∞, f(x) → +∞.

Front

What is the end behavior of a polynomial with a positive leading coefficient and an odd degree?

Back

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

Front

What is the end behavior of a polynomial with a negative leading coefficient and an even degree?

Back

As x → ±∞, f(x) → -∞.

Front

What is the end behavior of a polynomial with a negative leading coefficient and an odd degree?

Back

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

Front

If f(x) = 3x^4 + 2x - 5, what is the end behavior as x → ∞?

Back

As x → ∞, f(x) → ∞.

Front

If f(x) = 3x^4 + 2x - 5, what is the end behavior as x → -∞?

Back

As x → -∞, f(x) → ∞.

Front

What does it mean if a polynomial's end behavior is described as x → ∞, y → -∞?

Back

It means that as x increases without bound, the value of f(x) decreases without bound.

Front

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

Back

The leading coefficient indicates whether the ends of the graph rise or fall as x approaches ±∞.

Front

How can you identify the degree of a polynomial?

Back

The degree of a polynomial is the highest power of x in the polynomial expression.