End Behavior

Front

What is the leading coefficient of a polynomial function?

Back

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

Front

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

Back

If the leading coefficient is positive, the function will rise to the right; if negative, it will fall to the right.

Front

What is the degree of a polynomial function?

Back

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

Front

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

Back

If the degree is even, both ends of the graph will either rise or fall together; if odd, one end will rise and the other will fall.

Front

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

Back

Both ends of the graph will rise as x approaches positive and negative infinity.

Front

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

Back

Both ends of the graph will fall as x approaches positive and negative infinity.

Front

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

Back

The left end of the graph will fall while the right end will rise.

Front

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

Back

The left end of the graph will rise while the right end will fall.

Front

What is the significance of the leading term in determining end behavior?

Back

The leading term dominates the behavior of the polynomial as x approaches positive or negative infinity.

Front

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

Back

By observing the direction in which the ends of the graph extend as x approaches positive and negative infinity.