End Behavior of Functions and Graph

Front

What is end behavior in the context of functions?

Back

End behavior describes the behavior 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

The end behavior of a polynomial function can be determined by the leading term's degree and its leading coefficient.

Front

What does it mean if a function has 'up, up' end behavior?

Back

'Up, up' end behavior means that as x approaches both negative and positive infinity, the function f(x) approaches positive infinity.

Front

What does it mean if a function has 'down, down' end behavior?

Back

'Down, down' end behavior means that as x approaches both negative and positive infinity, the function f(x) approaches negative infinity.

Front

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

Back

The leading coefficient determines whether the ends of the graph rise or fall; a positive leading coefficient results in 'up' behavior, while a negative leading coefficient results in 'down' behavior.

Front

What is the end behavior of the function f(x) = 1 + 3x^2?

Back

The end behavior is 'up, up' as both x approaches negative and positive infinity, f(x) approaches positive infinity.

Front

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

Back

The end behavior is 'down, down' as both x approaches negative and positive infinity, f(x) approaches negative infinity.

Front

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

Back

Even-degree polynomials have the same end behavior on both sides, while odd-degree polynomials have opposite end behaviors.

Front

What does it mean if a function has 'up, down' end behavior?

Back

'Up, down' end behavior means that as x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity.

Front

What is the end behavior of the function f(x) = 1 - x^2?

Back

The end behavior is 'down, down' as both x approaches negative and positive infinity, f(x) approaches negative infinity.