Increasing and Decreasing Intervals

Front

What are increasing intervals in a function?

Back

Increasing intervals are ranges of x-values where the function's output (y-value) increases as x increases.

Front

What are decreasing intervals in a function?

Back

Decreasing intervals are ranges of x-values where the function's output (y-value) decreases as x increases.

Front

Define constant intervals in a function.

Back

Constant intervals are ranges of x-values where the function's output (y-value) remains the same as x increases.

Front

How do you identify increasing intervals from a graph?

Back

Look for sections of the graph where the curve rises as you move from left to right.

Front

How do you identify decreasing intervals from a graph?

Back

Look for sections of the graph where the curve falls as you move from left to right.

Front

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

Back

It represents all x-values less than or equal to -3.

Front

What does the notation \( [2, \infty) \) represent?

Back

It represents all x-values greater than or equal to 2.

Front

What is the significance of endpoints in interval notation?

Back

Endpoints indicate whether the interval includes the boundary value (closed interval) or not (open interval).

Front

How can you express the increasing interval of a function that starts at -3 and goes to infinity?

Back

The increasing interval can be expressed as \( [-3, \infty) \).

Front

What is the increasing interval for the function if it rises until x = 2?

Back

The increasing interval is \( (-\infty, 2) \).