Key Features of Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the domain of a function?

Back

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

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.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of f(x) decreases.

Front

How do you identify the intervals of increase and decrease on a graph?

Back

Intervals of increase and decrease can be identified by analyzing the slope of the graph: positive slope indicates increasing, negative slope indicates decreasing.

Front

What is an interval notation?

Back

Interval notation is a way of writing subsets of the real number line, using parentheses and brackets to indicate whether endpoints are included.

Front

What does [a, b] represent in interval notation?

Back

The notation [a, b] represents a closed interval that includes both endpoints a and b.

Front

What does (a, b) represent in interval notation?

Back

The notation (a, b) represents an open interval that does not include the endpoints a and b.

Front

What is the significance of critical points in a function?

Back

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