Polynomial End Behavior

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What does the degree of a polynomial indicate?

Back

The degree of a polynomial indicates the highest power of the variable in the polynomial.

Front

How does the sign of the leading coefficient affect end behavior for even-degree polynomials?

Back

For even-degree polynomials, if the leading coefficient is positive, both ends of the graph rise to +∞. If negative, both ends fall to -∞.

Front

How does the sign of the leading coefficient affect end behavior for odd-degree polynomials?

Back

For odd-degree polynomials, if the leading coefficient is positive, the left end falls to -∞ and the right end rises to +∞. If negative, the left end rises to +∞ and the right end falls to -∞.

Front

What is the end behavior of the polynomial y = -7x^4 + 3x^3 - 3x^2 + 5x - 8?

Back

As x → -∞, f(x) → -∞; As x → +∞, f(x) → -∞.

Front

What is the end behavior of the polynomial y = -5x^3 + 4x^2 + 5x - 8?

Back

As x → -∞, f(x) → +∞; 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) → -∞; 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) → -∞; As x → +∞, f(x) → -∞.

Front

Define end behavior in the context of polynomials.

Back

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

Front

What is the significance of the degree of a polynomial in determining end behavior?

Back

The degree of a polynomial determines the overall shape of the graph and how it behaves at the ends.