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 further discusses how to determine if the relation is a function by checking if each input has exactly one output. The tutorial uses mapping and graphical representation to illustrate these concepts, including the vertical line test, which helps identify if a relation is a function by checking if a vertical line intersects the graph more than once.

What is the domain of a relation?

• The set of all possible outputs

• The set of all first values in the ordered pairs

• The set of all possible ordered pairs

• The set of all second values in the ordered pairs

How should the range values be presented?

• In descending order

• In ascending order

• In random order

• In alphabetical order

What defines a function in terms of input and output?

• Each input has exactly one output

• Each output has exactly one input

• Each output has multiple inputs

• Each input has multiple outputs

Why is the given relation not a function?

• The input has no outputs

• The input has exactly one output

• The input has multiple outputs

• The output has multiple inputs

What does a mapping diagram show in a relation?

• The relation between ordered pairs

• The relation between outputs only

• The relation between inputs only

• The relation between inputs and outputs

In a mapping diagram, what does an arrow from an input to an output represent?

• An output with no input

• An input with no output

• A relation between an input and an output

• A relation between two outputs

How many outputs does the input of 8 have in the given relation?

• Four

• Three

• Two

• One

What is the purpose of the vertical line test?

• To determine if a relation is one-to-one

• To determine if a graph is quadratic

• To determine if a relation is a function

• To determine if a graph is linear

What does it mean if a vertical line intersects a graph at more than one point?

• The relation is not a function

• The graph is linear

• The graph is quadratic

• The relation is a function

What does the vertical line test indicate about the input of 8?

• It has no inputs

• It has multiple outputs

• It has exactly one output

• It has no outputs