Functions and Relations Review

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). Relations can be functions or not functions.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the Vertical Line Test.

Front

What does it mean for a set of ordered pairs to be a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value) with different second elements (y-values).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method used to determine if a graph is a function. If a vertical line crosses the graph more than once, it is not a function.

Front

What is the output of the function f(x) = 2x + 1 when x = 3?

Back

f(3) = 2(3) + 1 = 7.

Front

What is the output of the function f(x) = x^2 when x = 4?

Back

f(4) = 4^2 = 16.

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). If any x-value has multiple y-values, it is not a function.

Front

Is the following set of ordered pairs a function? {(1, 2), (1, 3), (2, 4)}

Back

No, it is not a function because the x-value 1 corresponds to two different y-values (2 and 3).

Front

What is an example of a function?

Back

An example of a function is f(x) = 3x - 5, where each input x has a unique output.