4.1 End Behavior of Polynomials

Front

What is the end behavior of a polynomial?

Back

The end behavior of a polynomial describes how the function behaves as x approaches positive or negative infinity.

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient determines the direction of the graph as x approaches positive or negative infinity.

Front

If the leading coefficient is positive and the degree is even, what is the end behavior?

Back

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

Front

If the leading coefficient is negative and the degree is odd, what is the end behavior?

Back

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

Front

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

Back

An even degree polynomial has the same end behavior on both sides of the graph.

Front

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

Back

An odd degree polynomial has opposite end behaviors on each side of the graph.

Front

How can you determine the degree of a polynomial?

Back

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

Front

What is the significance of the sign of the leading coefficient?

Back

The sign of the leading coefficient indicates whether the ends of the graph rise or fall.

Front

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

Back

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

Front

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

Back

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