Relations & Functions

Front

What is a function in mathematics?

Back

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

Front

How can you determine if a table represents a function?

Back

A table represents a function if each x-value is paired with exactly one y-value. If any x-value is paired with multiple y-values, it is not a function.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and can be represented by a straight line, while nonlinear functions do not have a constant rate of change and can be represented by curves.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is a one-to-one function?

Back

A one-to-one function is a function in which each output (y-value) is paired with exactly one input (x-value), meaning no two different x-values map to the same y-value.

Front

What is a domain in the context of functions?

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 a range in the context of functions?

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 if, as the x-values increase, the y-values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the x-values increase, the y-values decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has the same output for every input.