End Behavior and Increasing/Decreasing Intervals

Front

What is end behavior in a graph?

Back

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

Front

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

Back

To determine the end behavior of a polynomial function, look at the leading term's degree and its leading coefficient.

Front

What does it mean if a graph approaches -∞ as x approaches -∞?

Back

It means that as the x-values decrease without bound, the y-values also decrease without bound.

Front

What does it mean if a graph approaches +∞ as x approaches +∞?

Back

It means that as the x-values increase without bound, the y-values also increase without bound.

Front

Define increasing interval in a function.

Back

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

Front

Define decreasing interval in a function.

Back

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

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 means the right end rises, while a negative one means it falls.

Front

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

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

Front

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

Back

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches -∞.

Front

What does it indicate if a function is decreasing on the interval (-1, ∞)?

Back

It indicates that for all x-values greater than -1, the function's output is getting smaller.