End Behavior of Functions

Front

What is end behavior in the context of functions?

Back

End behavior describes the behavior of the graph of a function as the input values (x) approach positive or negative infinity.

Front

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

Back

To determine the end behavior of a polynomial function, look at the leading term's degree and coefficient. If the degree is even, both ends will go in the same direction; if odd, they will go in opposite directions.

Front

What does it mean if a function approaches positive infinity as x approaches positive infinity?

Back

It means that the values of the function (y) increase without bound as x increases.

Front

What does it mean if a function approaches negative infinity as x approaches negative infinity?

Back

It means that the values of the function (y) decrease without bound as x decreases.

Front

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

Back

The leading coefficient determines the direction of the graph's ends: if positive, the right end goes up; if negative, the right end goes down.

Front

How can you identify the left end behavior of a function?

Back

The left end behavior is identified by analyzing the function's behavior as x approaches negative infinity.

Front

What is the end behavior of a function if it approaches positive infinity as x approaches negative infinity?

Back

This indicates that the left end of the graph rises indefinitely while the right end may behave differently.

Front

What is the end behavior of a function if it approaches negative infinity as x approaches positive infinity?

Back

This indicates that the right end of the graph falls indefinitely while the left end may behave differently.

Front

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

Back

The degree of a polynomial affects whether the ends of the graph go up or down and whether they go in the same or opposite directions.

Front

What is the end behavior of a quadratic function with a positive leading coefficient?

Back

As x approaches positive or negative infinity, y approaches positive infinity.