Relations and 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) and an output (y).

Front

What is a function?

Back

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

Front

How do you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-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

If g(x) = x^2 - 4, what is g(3)?

Back

g(3) = 3^2 - 4 = 9 - 4 = 5.

Front

If f(x) = 2x + 3, what is f(5)?

Back

f(5) = 2(5) + 3 = 10 + 3 = 13.

Front

What is an ordered pair?

Back

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

Front

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

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.