Exploring the Basics of Functions

The video tutorial introduces the concept of functions, explaining two-variable data and how to represent it using ordered pairs and mappings. It defines relations and functions, emphasizing the importance of each input having a single output. The vertical line test is introduced as a method to determine if a graph represents a function. Examples are provided to illustrate these concepts, including real-world analogies like social security numbers and birthdays.

What is the independent variable in the example of alligator age and length?

• Height of the alligator

• Length of the alligator

• Age of the alligator

• Weight of the alligator

How are ordered pairs represented?

• Using square brackets

• Using parentheses

• Using curly braces

• Using angle brackets

What is the domain in a set of ordered pairs?

• The y-values

• The x-values

• The dependent variables

• The output values

What makes a relation a function?

• Each output has multiple inputs

• Each input has multiple outputs

• Each output has exactly one input

• Each input has exactly one output

Which of the following is NOT a characteristic of a function?

• Each input can have multiple outputs

• Each output can have multiple inputs

• Each input has exactly one output

• Each input is paired with one output

What does the vertical line test help determine?

• If a graph has multiple outputs

• If a graph has multiple inputs

• If a graph is a function

• If a graph is a relation

In the vertical line test, what indicates that a graph is NOT a function?

• The vertical line touches the graph at exactly one point

• The vertical line touches the graph at multiple points

• The vertical line does not touch the graph

• The vertical line touches the graph at no points

Which of the following is an example of a function?

• A social security number assigned to one person

• A birthday shared by multiple people

• A social security number assigned to multiple people

• A name shared by multiple people

Why is a birthday not a function in the given example?

• Because birthdays are not numerical

• Because birthdays cannot be mapped

• Because each birthday is unique

• Because multiple people can have the same birthday

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

• The graph represents a function

• The graph does not represent a function

• The graph is a relation

• The graph is a mapping