End Behavior

Front

What is end behavior in mathematics?

Back

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

Front

What does it mean when we say a function's end behavior is 'up and up'?

Back

It means that as x approaches both negative infinity and positive infinity, the value of y approaches positive infinity.

Front

What does it mean when we say a function's end behavior is 'down and down'?

Back

It means that as x approaches both negative infinity and positive infinity, the value of y approaches negative infinity.

Front

For the function y = x^2, what is the end behavior?

Back

As x → -∞, y → ∞ and as x → ∞, y → ∞.

Front

For the function y = -x^2, what is the end behavior?

Back

As x → -∞, y → -∞ and as x → ∞, y → -∞.

Front

What is the end behavior of a function if it approaches negative infinity on the left and negative infinity on the right?

Back

The end behavior is described as 'down and down'.

Front

What is the end behavior of a function if it approaches positive infinity on the left and positive infinity on the right?

Back

The end behavior is described as 'up and up'.

Front

If a function has end behavior of 'up and down', what does that indicate?

Back

It indicates that as x approaches negative infinity, y approaches positive infinity, and as x approaches positive infinity, y approaches negative infinity.

Front

What is the significance of analyzing end behavior in functions?

Back

Analyzing end behavior helps in understanding the overall trend of the function and predicting its behavior at extreme values.

Front

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

Back

The end behavior can be determined by the leading term of the polynomial and its degree.