End Behavior of Functions

Front

What is end behavior of a function?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

How do you determine the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by its leading term. For example, if the leading term is positive and has an even degree, the function will approach positive infinity as x approaches both positive and negative infinity.

Front

What does it mean if a function approaches -∞ as x approaches -∞?

Back

It means that as the input values decrease without bound, the output values of the function also decrease without bound.

Front

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

Back

The leading coefficient indicates the direction of the end behavior. A positive leading coefficient means the function will rise to positive infinity, while a negative leading coefficient means it will fall to negative infinity.

Front

Back

Front

Back

Front

Back

Front

How can you graphically determine the end behavior of a function?

Back

You can analyze the graph of the function to see the direction it heads as x approaches positive or negative infinity.

Front

Back

It indicates that as the input values decrease without bound, the output values of the function increase without bound.

Front

Back