Function Features

Front

What is the minimum value of a function?

Back

The minimum value of a function is the lowest point on its graph, representing the smallest output value (y-value) for any input (x-value).

Front

How do you determine the interval of decrease for a function?

Back

The interval of decrease is found by identifying the x-values where the function's output (y-value) is decreasing as x increases. This is typically where the derivative of the function is negative.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain (input values).

Front

How do you find the interval of increase for a function?

Back

The interval of increase is determined by identifying the x-values where the function's output (y-value) is increasing as x increases. This occurs where the derivative of the function is positive.

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 output value at the second point is greater than the output value 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 output value at the second point is less than the output value at the first point.

Front

What is the significance of critical points in a function?

Back

Critical points are values of x where the derivative is zero or undefined. They are important for determining local maxima, minima, and intervals of increase or decrease.

Front

How do you identify local maxima and minima?

Back

Local maxima and minima can be identified using the first derivative test, which involves analyzing the sign of the derivative before and after critical points.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints (e.g., (a, b)), while a closed interval includes its endpoints (e.g., [a, b]).

Front

What is a function's domain?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.