End Behavior of Polynomials

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

If a polynomial has a positive leading coefficient and an odd degree, what is its end behavior?

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches +∞.

Front

If a polynomial has a negative leading coefficient and an even degree, what is its end behavior?

Back

As x approaches -∞, f(x) approaches -∞; as x approaches +∞, f(x) approaches -∞.

Front

What is the maximum number of turning points a polynomial can have?

Back

The maximum number of turning points of a polynomial is one less than its degree.

Front

For the polynomial f(x) = 5x^8 - 10x^6 - 4x^4 + 24, what is the maximum number of turning points?

Back

7 turning points.

Front

What is the degree of a polynomial?

Back

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

Front

What is a leading coefficient?

Back

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

Front

If a polynomial has an even degree and a positive leading coefficient, what is its end behavior?

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

What does it mean for a polynomial to have a relative maximum?

Back

A relative maximum is a point where the polynomial reaches a peak value compared to its immediate surroundings.

Front

How do you identify the end behavior of a polynomial from its graph?

Back

Look at the direction the graph goes as x approaches -∞ and +∞.