Function Intervals 1

Front

What is a function interval?

Back

A function interval is a range of values for the independent variable (usually x) over which a function exhibits a certain behavior, such as being increasing, decreasing, or constant.

Front

Define 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

Define 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

What does it mean for a function to be constant over an interval?

Back

A function is constant over an interval if it produces the same output (y-value) for every input (x-value) within that interval.

Front

How do you identify a nonlinear function?

Back

A nonlinear function does not form a straight line when graphed. It may curve or change direction.

Front

What is the notation for an open interval?

Back

An open interval is denoted using parentheses, e.g., (a, b), meaning that a and b are not included in the interval.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted using brackets, e.g., [a, b], meaning that a and b are included in the interval.

Front

How can you determine if a function is increasing on a graph?

Back

A function is increasing on a graph if, as you move from left to right, the graph rises.

Front

How can you determine if a function is decreasing on a graph?

Back

A function is decreasing on a graph if, as you move from left to right, the graph falls.

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.