Relations, Domain, Range, Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

What is a function?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for a function.

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

Given the relation {(1,2), (2,3), (1,4)}, is it a function?

Back

No, because the x-value 1 is paired with both 2 and 4.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a coordinate system.

Front

If the function is f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once.

Front

What is the vertical line test?

Back

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