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

How does the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive, the polynomial will rise to infinity as x approaches both positive and negative infinity. If it is negative, the polynomial will fall to negative infinity as x approaches both positive and negative infinity.

Front

What is the end behavior of the polynomial function f(x) = 3x + 2?

Back

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

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 the end behavior of the polynomial function j(x) = 9x^4 - 2?

Back

As x → -∞, j(x) → ∞; As x → ∞, j(x) → ∞.

Front

What does it mean if a polynomial has an even degree?

Back

A polynomial with an even degree will have the same end behavior on both sides: either both ends rise or both ends fall.

Front

What does it mean if a polynomial has a negative leading coefficient?

Back

A polynomial with a negative leading coefficient will fall to negative infinity on one side and rise to positive infinity on the other side if it has an odd degree.

Front

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

Back

The end behavior of a polynomial helps to determine the overall shape of the graph and how it behaves as x approaches positive or negative infinity.

Front

How can you determine the end behavior of a polynomial function from its graph?

Back

You can determine the end behavior by observing the direction in which the graph heads as x approaches positive and negative infinity.

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.