intervals of increase/decrease

Front

What is an increasing interval?

Back

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

Front

What is a decreasing interval?

Back

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

Front

How do you determine if a function is increasing or decreasing?

Back

You can determine if a function is increasing or decreasing by analyzing its derivative: if the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What does it mean for a function to be constant?

Back

A function is constant over an interval if its output (y-values) does not change as x varies within that interval.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What is a non-function?

Back

A non-function is a relation where at least one input (x-value) is associated with more than one output (y-value).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output (y) values that the function can produce.

Front

How do you find the range of a function?

Back

To find the range, analyze the output values of the function for all possible input values.

Front

Back

This notation represents an interval of x-values from -1.5 to 1, where -1.5 is not included and 1 is included.

Front

What is the significance of endpoints in an interval?

Back

Endpoints indicate the boundaries of the interval; whether they are included or excluded affects the interval's definition.