Understanding Functions and Relations

This video tutorial explains the difference between relations and functions, using ordered pairs, mapping diagrams, tables, and graphs. It covers the concepts of domain and range, and how to identify functions by ensuring each input has exactly one output. The tutorial includes examples and a real-world scenario to illustrate these concepts.

What is the domain in a relation?

• The set of all functions

• The set of all ordered pairs

• The set of all input values

• The set of all output values

How can a relation be represented?

• Only through graphs

• Only through tables

• Only through mapping diagrams

• Through ordered pairs, mapping diagrams, tables, and graphs

What characterizes a discrete graph?

• A continuous line

• A set of real numbers

• Individual points

• A curve

What is a key feature of a function?

• Exactly one output for every input

• Multiple inputs for a single output

• Multiple outputs for a single input

• No outputs for any input

In a function, what happens if an input has more than one output?

• It becomes a relation, not a function

• It becomes a discrete graph

• It becomes a continuous graph

• It remains a function

What is a common misunderstanding about functions?

• Functions are the same as relations

• Functions can have exactly one output for every input

• Functions must have the same output for every input

• Functions can have multiple outputs for a single input

In the summer job example, what is the independent variable?

• The amount of money earned

• The number of hours worked

• The hourly wage

• The total weekly earnings

What is the range in the summer job example?

• 12 dollars per hour

• 0 to 36 dollars

• 0 to 120 dollars

• 0 to 10 hours

Why is the summer job example considered a function?

• The hours worked are the same for every earning

• Each hour worked corresponds to multiple earnings

• Each hour worked corresponds to a specific amount of money earned

• The earnings are the same for every hour worked

What does the range depend on in the summer job example?

• The number of hours worked

• The hourly wage

• The total weekly earnings

• The number of days worked