Polynomial End Behavior

Front

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

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches positive infinity; as x approaches negative infinity, f(x) approaches positive infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

Front

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

Back

As x approaches positive infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches negative infinity.

Front

Define the degree of a polynomial.

Back

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

Front

What does the leading coefficient of a polynomial indicate?

Back

The leading coefficient is the coefficient of the term with the highest degree, and it affects the end behavior of the polynomial.

Front

How can you determine if a polynomial is even or odd based on its degree?

Back

A polynomial is even if its degree is even and odd if its degree is odd.

Front

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

Back

The sign of the leading coefficient (positive or negative) determines whether the ends of the graph rise or fall.

Front

What is the general form of a polynomial function?

Back

A polynomial function is generally expressed as f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n is the leading coefficient.

Front

What is the relationship between the degree of a polynomial and the number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.