Exploring Functions and Their Domain/Range

This video tutorial introduces the concept of functions and relations, explaining how each input must have a unique output to qualify as a function. It covers methods to identify functions, including the vertical line test for graphs. The tutorial also explains domain and range, providing examples and highlighting techniques to determine these for given functions and graphs.

What is a function in terms of relations?

• A relation where each input has exactly one output

• A relation where each output has exactly one input

• A relation where inputs and outputs are the same

• A relation with no inputs

In the given example, why is the relation where -1 goes to 4 and 3 goes to 11 and 15 not a function?

• Because 11 goes to 12

• Because -1 goes to 4

• Because 15 is an output

• Because 3 goes to two different outputs

How can you determine if a relation is a function by highlighting inputs and outputs?

• By ensuring inputs do not repeat

• By ensuring inputs and outputs are the same

• By ensuring both inputs and outputs do not repeat

• By ensuring outputs do not repeat

Why is the relation with inputs 4, 8, 6, 4, and 5 not a function?

• Because 4 is an input

• Because 8 is an input

• Because 4 goes to two different outputs

• Because 5 is an input

What is the vertical line test used for?

• To determine if a relation is a function

• To determine if a graph represents a function

• To determine the range of a function

• To determine the domain of a function

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

• The graph represents a function

• The graph does not represent a function

• The graph has no inputs

• The graph has no outputs

What is the domain of a function?

• The set of all vertical lines

• The set of all points on a graph

• The set of all inputs

• The set of all outputs

How is the range of a function defined?

• The set of all points on a graph

• The set of all outputs

• The set of all inputs

• The set of all horizontal lines

In a graph with arrows indicating it continues, what is the domain and range?

• Only integers

• Only negative numbers

• Only positive numbers

• All real numbers

How do you represent the domain and range of a graph that ends using inequalities?

• Using equal signs

• Using inequality signs with closed circles

• Using curly brackets

• Using parentheses