End Behavior

Front

What is End Behavior in mathematics?

Back

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

Front

What does it mean when we say x→∞ and y→∞?

Back

It means that as x increases without bound, the value of y also increases without bound.

Front

What does it mean when we say x→-∞ and y→-∞?

Back

It means that as x decreases without bound, the value of y also decreases without bound.

Front

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

Back

The end behavior of a polynomial function can be determined by the leading term of the function.

Front

What is the end behavior of the function f(x) = x^2?

Back

As x→-∞, y→∞ and as x→∞, y→∞.

Front

What is the end behavior of the function f(x) = -x^2?

Back

As x→-∞, y→-∞ and as x→∞, y→-∞.

Front

What is the end behavior of the function f(x) = x^3?

Back

As x→-∞, y→-∞ and as x→∞, y→∞.

Front

What is the end behavior of the function f(x) = -x^3?

Back

As x→-∞, y→∞ and as x→∞, y→-∞.

Front

What is the end behavior of the function f(x) = x^4?

Back

As x→-∞, y→∞ and as x→∞, y→∞.

Front

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

Back

The sign of the leading coefficient determines whether the ends of the graph rise or fall.