Functions - Graphs

Front

What does it mean for a function to be increasing in an interval?

Back

A function is increasing in an interval if, as the input values (x) increase, the output values (f(x)) also increase.

Front

What does it mean for a function to be decreasing in an interval?

Back

A function is decreasing in an interval if, as the input values (x) increase, the output values (f(x)) decrease.

Front

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

Back

A function is constant in an interval if the output values (f(x)) do not change as the input values (x) change.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is an interval in the context of functions?

Back

An interval is a range of x-values over which a function is analyzed, often denoted as (a, b), [a, b], or [a, b).

Front

What is the difference between an increasing function and a decreasing function?

Back

An increasing function has a positive slope, while a decreasing function has a negative slope.

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

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 (f(x)) that the function can produce.