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 positive or 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 or 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 observing 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 negative?

Back

It indicates that 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

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

Back

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

Front

How does the leading coefficient affect the graph of a polynomial function?

Back

The leading coefficient affects the direction of the graph's end behavior and the steepness of the graph.