End Behavior and vocab

Front

What is the end behavior of a polynomial function?

Back

The end behavior of a polynomial function describes how the function behaves as the input values approach positive or negative infinity. It is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial affects its end behavior: if the degree is even, both ends of the graph will either rise or fall together; if the degree is odd, one end will rise while the other falls.

Front

What is a leading coefficient in a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial. It influences the end behavior of the polynomial.

Front

How can you determine if a polynomial is even or odd?

Back

A polynomial is even if all the exponents of its terms are even numbers, and it is odd if at least one term has an odd exponent.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the polynomial expression.

Front

What is the leading coefficient of the polynomial 3x^2 - 2x + 5?

Back

The leading coefficient is 3, which is the coefficient of the term with the highest degree (x^2).

Front

How do you find the number of terms in a polynomial?

Back

The number of terms in a polynomial is determined by counting the distinct terms in the polynomial expression, regardless of their coefficients.

Front

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

Back

The end behavior will show that as x approaches positive infinity, the function approaches negative infinity, and as x approaches negative infinity, the function approaches positive infinity.

Front

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

Back

The sign of the leading coefficient indicates whether the ends of the polynomial graph will rise or fall. A positive leading coefficient means the right end rises, while a negative leading coefficient means the right end falls.

Front

What does it mean for a polynomial to have an even degree?

Back

A polynomial has an even degree if the highest exponent of its variable is an even number, resulting in both ends of the graph rising or falling together.