Inc/Dec Intervals & End Behavior Check

Front

What is an increasing interval in a function?

Back

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

Front

What is a decreasing interval in a function?

Back

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

Front

How do you identify increasing and decreasing intervals from a graph?

Back

Increasing intervals are where the graph rises from left to right, while decreasing intervals are where the graph falls.

Front

What does the notation \( (-\infty, -3) \) represent?

Back

It represents all x-values less than -3.

Front

What does the notation \( (1, \infty) \) represent?

Back

It represents all x-values greater than 1.

Front

What is end behavior in the context of functions?

Back

End behavior describes how a function behaves as x approaches positive or negative infinity.

Front

What does it mean if a function approaches \( \infty \) as \( x \to -\infty \)?

Back

It means that as x decreases without bound, the function's output increases without bound.

Front

What does it mean if a function approaches \( -\infty \) as \( x \to \infty \)?

Back

It means that as x increases without bound, the function's output decreases without bound.

Front

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

Back

The end behavior can be determined by the leading term of the polynomial.

Front

What is the significance of critical points in determining intervals of increase or decrease?

Back

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