Function Features

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than at the first point.

Front

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints, which can be open (not including endpoints) or closed (including endpoints).

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

What is a minimum of a function?

Back

The minimum of a function is the lowest point on the graph of the function, representing the smallest output value.

Front

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

Back

To determine where a function is increasing or decreasing, analyze the slope of the function's graph or use the first derivative test.

Front

What is the significance of the first derivative of a function?

Back

The first derivative of a function indicates the rate of change of the function; it helps identify increasing and decreasing intervals.

Front

What does it mean for a function to have no x-intercept?

Back

A function has no x-intercept if it never crosses the x-axis, meaning it does not have any real solutions where the output is zero.

Front

What is an interval of decrease?

Back

An interval of decrease is a range of x-values where the function's output values are getting smaller as x increases.