End Behavior of Functions

Front

What is the end behavior of a function?

Back

The end behavior of a function describes how the function behaves as the input values (x) approach positive or negative infinity.

Front

As x approaches positive infinity, what does y approach for a function that rises indefinitely?

Back

y approaches positive infinity.

Tags

CCSS.HSF-IF.C.7E

Front

As x approaches negative infinity, what does y approach for a function that falls indefinitely?

Back

y approaches negative infinity.

Tags

CCSS.HSF-IF.C.7E

Front

What does it mean when we say 'as x approaches negative infinity'?

Back

It refers to the behavior of the function as the x-values decrease without bound.

Front

What does it mean when we say 'as x approaches positive infinity'?

Back

It refers to the behavior of the function as the x-values increase without bound.

Front

If a function approaches a specific value as x approaches positive infinity, what is this value called?

Back

This value is called the horizontal asymptote.

Tags

CCSS.HSF-IF.C.7D

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

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

Front

What is the leading term of a polynomial?

Back

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

Front

For a polynomial function with an even degree and a positive leading coefficient, what is the end behavior?

Back

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