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 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 positive leading coefficient?

Back

As x approaches both positive and 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 both positive and negative infinity, f(x) approaches negative infinity.

Front

How can you determine the degree of a polynomial from its graph?

Back

The degree can be determined by the number of times the graph crosses the x-axis and the overall shape of the graph.

Front

What does it mean if a polynomial has a leading coefficient that is positive?

Back

The graph of the polynomial will rise to the right as x approaches positive infinity.

Front

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

Back

The graph of the polynomial will fall to the right as x approaches positive infinity.

Front

What is the significance of the degree of a polynomial in relation to its end behavior?

Back

The degree determines whether the end behavior is similar on both ends (even degree) or opposite (odd degree).

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.

Front

How can you identify the leading coefficient of a polynomial from its graph?

Back

The leading coefficient can be inferred from the direction of the graph as x approaches positive or negative infinity.