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) is rising 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) is falling as x increases.

Front

Define positive interval in the context of functions.

Back

A positive interval is a range of x-values where the function's output (y-values) is greater than zero.

Front

Define negative interval in the context of functions.

Back

A negative interval is a range of x-values where the function's output (y-values) is less than zero.

Front

How do you identify increasing intervals from a graph?

Back

Increasing intervals can be identified on a graph where the slope of the tangent line is positive.

Front

How do you identify decreasing intervals from a graph?

Back

Decreasing intervals can be identified on a graph where the slope of the tangent line is negative.

Front

What does it mean if a function is increasing on the interval (-∞, 2]?

Back

It means that for all x-values less than or equal to 2, the function's output is increasing.

Front

What does it mean if a function is decreasing on the interval (-∞, -3)?

Back

It means that for all x-values less than -3, the function's output is decreasing.

Front

What is the significance of critical points in determining intervals?

Back

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

Front

How can you find the increasing and decreasing intervals algebraically?

Back

By finding the derivative of the function and determining where it is positive (increasing) or negative (decreasing).