Positive/Negative and Increasing/Decreasing Intervals

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) increases 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) decreases as x increases.

Front

How do you identify increasing intervals on a graph?

Back

Look for sections of the graph where the slope is positive (the graph rises as you move from left to right).

Front

How do you identify decreasing intervals on a graph?

Back

Look for sections of the graph where the slope is negative (the graph falls as you move from left to right).

Front

What does it mean if a function is constant on an interval?

Back

A constant interval is where the function's output does not change as x changes; the slope is zero.

Front

What is the notation for an interval?

Back

Intervals are often written in parentheses (a, b) for open intervals or brackets [a, b] for closed intervals.

Tags

CCSS.6.EE.B.8

Front

What is the significance of endpoints in intervals?

Back

Endpoints can indicate where a function changes from increasing to decreasing or vice versa; they may or may not be included in the interval.

Front

What is the difference between open and closed intervals?

Back

Open intervals (a, b) do not include endpoints a and b, while closed intervals [a, b] include both endpoints.

Tags

CCSS.6.EE.B.8

Front

How do you find the increasing intervals algebraically?

Back

Set the derivative of the function greater than zero and solve for x.

Front

How do you find the decreasing intervals algebraically?

Back

Set the derivative of the function less than zero and solve for x.