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 if a function's end behavior is 'up/down'?

Back

It means that as x approaches infinity, the function goes up, and as x approaches negative infinity, the function goes down.

Front

What is the leading coefficient of a polynomial?

Back

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

Front

How does the leading coefficient affect the end behavior of a polynomial function?

Back

If the leading coefficient is positive and the degree is even, the end behavior is up/up. If it is negative and the degree is even, the end behavior is down/down. If the degree is odd, a positive leading coefficient results in up/down, while a negative leading coefficient results in down/up.

Front

Back

The end behavior is up/down.

Front

What does it mean if a function goes down on the left?

Back

It means that as x approaches negative infinity, the function's value approaches negative infinity.

Front

What is the significance of the degree of a polynomial in determining end behavior?

Back

The degree of a polynomial determines the number of times the graph can change direction and influences the end behavior.

Front

If a polynomial has an even degree and a positive leading coefficient, what is its end behavior?

Back

The end behavior is up/up.

Front

If a polynomial has an odd degree and a negative leading coefficient, what is its end behavior?

Back

The end behavior is down/up.

Front

Back

It signifies that as x approaches infinity, the function f(x) also approaches infinity.