Polynomial End Behavior

Front

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

Back

As x approaches positive or negative infinity, the polynomial approaches positive infinity.

Front

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

Back

As x approaches positive or negative infinity, the polynomial approaches negative infinity.

Front

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

Back

As x approaches positive infinity, the polynomial approaches positive infinity, and as x approaches negative infinity, it approaches negative infinity.

Front

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

Back

As x approaches positive infinity, the polynomial approaches negative infinity, and as x approaches negative infinity, it approaches positive infinity.

Front

Define 'leading coefficient' in 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 can you determine the degree of a polynomial from its graph?

Back

The degree can often be inferred from the number of turning points in the graph; a polynomial of degree n can have at most n-1 turning points.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

What is the significance of the end behavior of a polynomial?

Back

The end behavior helps predict how the polynomial behaves as the input values become very large or very small.

Front

What is a turning point in the context of polynomial graphs?

Back

A turning point is a point where the graph changes direction from increasing to decreasing or vice versa.