Determining Functions: Key Concepts and Tests

This video tutorial explains how to determine if a relationship is a function. It covers the definition of a function, using a function machine as an example, and explains the concept of domain and range. The tutorial also demonstrates how to check if a relation is a function using tables, mappings, and the vertical line test on graphs. It concludes with a discussion on equations and their role in identifying functions.

Which graph represents a function?

• Neither graph

• The graph on the right

• The graph on the left

• Both graphs

What does the function machine do to its inputs?

• Divides by 5

• Subtracts 3

• Adds 4

• Multiplies by 2

What is the definition of a function in algebra?

• A relation where each input is paired with multiple outputs

• A relation where each output is paired with multiple inputs

• A relation where each input is paired with exactly one output

• A relation where each output is paired with exactly one input

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

• Inequalities

• Mappings

• Tables

• Ordered pairs

How can you determine if a table represents a function?

• By checking for repeating y values

• By checking for repeating outputs

• By checking for repeating x values

• By checking for repeating inputs

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

• Single arrow from different inputs to different outputs

• Single arrow from one input to one output

• Multiple arrows from different inputs to one output

• Multiple arrows from one input to different outputs

What is the vertical line test used for?

• To check if a table represents a function

• To check if a graph represents a function

• To check for repeating x values

• To check for repeating y values

Which of the following graphs passes the vertical line test?

• A graph that intersects a vertical line at three points

• A graph that intersects a vertical line at one point

• A graph that intersects a vertical line at two points

• A graph that does not intersect a vertical line

Which equation does NOT represent a function?

• y = x^2

• x = 5

• y = sqrt(x)

• y = 2x + 3

What is a key characteristic of a function in terms of x and y values?

• No repeating y values with the same x values

• No repeating x values with the same y values

• No repeating x values with different y values

• No repeating y values with different x values