End behavior/Increasing & decreasing intervals

Front

What is end behavior in graphing functions?

Back

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

Front

Define increasing interval.

Back

An increasing interval is a range of x-values where the function's output (y) is rising as x increases.

Front

Define decreasing interval.

Back

A decreasing interval is a range of x-values where the function's output (y) is falling as x increases.

Front

What does it mean if a function approaches infinity as x approaches infinity?

Back

It means that the function's values grow without bound as x increases.

Front

What does it mean if a function approaches negative infinity as x approaches negative infinity?

Back

It means that the function's values decrease without bound as x decreases.

Front

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

Back

The end behavior of a polynomial function is 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

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

Back

As x approaches ±∞, y approaches +∞.

Front

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

Back

As x approaches +∞, y approaches -∞ and as x approaches -∞, y approaches +∞.

Front

What is the significance of critical points in determining increasing and decreasing intervals?

Back

Critical points are where the derivative is zero or undefined, indicating potential changes in increasing or decreasing behavior.