Understanding Relations and Functions

The video tutorial explains how to find the domain and range of a relation given as a set of ordered pairs. It describes the domain as the set of all possible inputs and the range as the set of all possible outputs. The tutorial then demonstrates how to determine if a relation is a function by ensuring each input has exactly one output, using a mapping method. It also introduces the vertical line test as a graphical method to verify if a relation is a function, ensuring that a vertical line does not intersect the graph more than once.

What is the domain of a relation?

• The set of all second values in ordered pairs

• The set of all ordered pairs

• The set of all possible inputs

• The set of all possible outputs

How should the values in the domain be listed?

• In any order

• From greatest to least

• From least to greatest

• In alphabetical order

What is the range of the relation given in the video?

• The set containing all first values

• The set containing all ordered pairs

• The set containing negative seven

• The set containing five, four, three, and two

What defines a function in terms of input and output?

• Each input has exactly one output

• Each input has multiple outputs

• Each output has exactly one input

• Each output has multiple inputs

In the mapping method, what does an arrow from an input to an output represent?

• A function with multiple outputs

• A relation between an input and an output

• An input with no output

• An output with no input

What would indicate that a relation is not a function in a mapping diagram?

• An output with two arrows pointing to different inputs

• An output with no arrows

• An input with two arrows pointing to different outputs

• An input with no arrows

What is the purpose of the vertical line test?

• To determine if a relation is a function

• To determine the range of a relation

• To determine the domain of a relation

• To determine if a relation is linear

According to the vertical line test, when is a relation not a function?

• When a vertical line does not intersect the graph

• When a vertical line intersects the graph at more than one point

• When a vertical line intersects the graph at exactly one point

• When a vertical line intersects the graph at zero points

What does it mean if a vertical line intersects a graph at zero points?

• The graph has no range

• The graph has no domain

• The graph is a function

• The graph is not a function

What conclusion can be drawn if a graph passes the vertical line test?

• The relation has no range

• The relation is a function

• The relation is not a function

• The relation has no domain