Graph End Behavior

Front

What is the Leading Coefficient Test?

Back

The Leading Coefficient Test is a method used to determine the end behavior of a polynomial function based on the sign and degree of its leading term.

Front

How does the degree of a polynomial affect its end behavior?

Back

The degree of a polynomial determines whether the ends of the graph rise or fall. Even degrees lead to the same behavior on both ends, while odd degrees lead to opposite behaviors.

Front

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

Back

The graph rises on both ends.

Front

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

Back

The graph falls on both ends.

Front

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

Back

The graph falls to the left and rises to the right.

Front

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

Back

The graph rises to the left and falls to the right.

Front

If a polynomial function has a leading term of -3x^4, what is its end behavior?

Back

The graph falls on both ends because it has an even degree and a negative leading coefficient.

Front

If a polynomial function has a leading term of 2x^3, what is its end behavior?

Back

The graph falls to the left and rises to the right because it has an odd degree and a positive leading coefficient.

Front

What does it mean for a polynomial to 'rise' or 'fall' at the ends?

Back

'Rising' means the graph goes upwards as it moves away from the origin, while 'falling' means the graph goes downwards.

Front

How can you determine the end behavior of a polynomial function without graphing it?

Back

You can determine the end behavior by analyzing the leading term's degree and coefficient.