Understanding Functions and Their Properties

This video tutorial introduces Unit 4, focusing on understanding functions, their vocabulary, and concepts. It explains the definition of functions, how they differ from relations, and introduces the vertical line test to identify functions. The tutorial covers domain and range, providing examples and exercises to reinforce learning. It also includes graphing functions and analyzing their properties, such as increasing, decreasing, and constant functions.

What is the primary focus of Unit 4?

• Understanding algebraic expressions

• Exploring calculus principles

• Understanding function vocabulary and concepts

• Learning about geometric shapes

In the context of an elevator, what does 'function' mean?

• The color of the elevator

• The speed of the elevator

• The design of the elevator

• What the elevator is designed to do

How can a relation be expressed?

• As a song

• As a paragraph

• As a mapping, table, graph, or description

• As a single number

What makes a relation a function?

• Each Y can correspond with multiple X's

• Each X can correspond with only one Y

• Each Y can correspond with only one X

• Each X can correspond with multiple Y's

What is the domain in a function?

• The set of numbers you get out

• The set of numbers you plug in

• The set of letters you use

• The set of symbols you use

In the example of hours worked and pay, what is the independent variable?

• The amount of pay

• The type of job

• The day of the week

• The number of hours worked

What does the vertical line test determine?

• If a graph is symmetrical

• If a graph represents a function

• If a graph is decreasing

• If a graph is increasing

What does the squish technique help find?

• The color of a graph

• The intercepts of a graph

• The domain and range of a function

• The slope of a line

How can you tell if a function is increasing?

• The graph goes down from left to right

• The graph forms a circle

• The graph stays constant

• The graph goes up from left to right

Are all functions relations?

• No, functions are not related to relations

• No, only some functions are relations

• Yes, all functions are sets of ordered pairs

• Yes, but only if they are linear