Exploring Functions and Relations in Mathematics

Mrs. Hayes introduces the concept of functions and relations, outlining the learning goals for the lesson. She explains the definition of a function as a rule that assigns each input to at most one output, emphasizing that x values cannot repeat. The lesson covers how to determine if a relation is a function using graphs, mappings, and tables. Examples are provided to illustrate when a relation is not a function, particularly when an x value corresponds to multiple y values. The video encourages students to pause and review the material as needed.

What is the learning goal for today?

• To memorize mathematical formulas

• To learn about calculus

• To explain and use the definition of a function

• To understand the history of functions

What is the definition of a function?

• A rule that converts an output into at most one input

• A rule that converts an input into multiple outputs

• A rule that converts an input into at most one output

• A rule that converts an output into multiple inputs

What does the domain of a function represent?

• The set of w values

• The set of y values

• The set of x values

• The set of z values

What does the range of a function represent?

• The set of y values

• The set of z values

• The set of x values

• The set of w values

In a graph, how can you tell if a relation is a function?

• Each y value has only one x value

• Each y value has multiple x values

• Each x value has only one y value

• Each x value has multiple y values

Why is the relation in the given graph not a function?

• Because each y value has only one x value

• Because each x value has only one y value

• Because an x value has more than one y value

• Because a y value has more than one x value

What does a mapping show in terms of functions?

• The relationship between z values and w values

• The relationship between x values and y values

• The relationship between w values and x values

• The relationship between y values and z values

In a mapping, what indicates that a relation is not a function?

• A y value maps to a single x value

• An x value maps to a single y value

• A y value maps to multiple x values

• An x value maps to multiple y values

How can you determine if a relation is a function using a table?

• By checking if each y value has multiple x values

• By checking if each x value has multiple y values

• By checking if each x value has only one y value

• By checking if each y value has only one x value

Why is the relation in the given table a function?

• Because each y value has multiple x values

• Because each x value has multiple y values

• Because each x value has only one y value

• Because each y value has only one x value