Gr12 Mathematics: Ch 2.1 Functions and Relations

What is the primary difference between a relation and a function?

A relation has a unique output for every input, while a function has multiple outputs for every input.

A relation associates one element of set A with multiple elements of set B, while a function associates one element of set A with exactly one element of set B. (correct)

A relation is defined for all elements of set A, while a function is defined only for some elements of set A.

A relation is one-to-one, while a function is many-to-one.

Which type of function maps multiple elements of the domain to the same element of the range?

One-to-Many Relation

Constant Function

Many-to-One Function (correct)

One-to-One Function

What is the graphical representation of a one-to-one function?

Every vertical line intersects the graph at most once. (correct)

Every horizontal line intersects the graph more than once.

Every vertical line intersects the graph more than once.

Every horizontal line intersects the graph at most once.

What is not a type of function?

One-to-Many Relation Signup and view all the answers

What is the range of a function?

The set of all outputs of the function. Signup and view all the answers

What is the main characteristic of a one-to-one function?

Each element of the domain maps to a unique element of the range. Signup and view all the answers

In a function, how many elements of the range can be associated with a single element of the domain?

Exactly one Signup and view all the answers

What is the key characteristic of a one-to-many relation?

At least one vertical line intersects the graph more than once Signup and view all the answers

Which of the following is an example of a many-to-one function?

A city and its population Signup and view all the answers

What is the purpose of a graphical representation of a function?

To visualize the relationship between the domain and range Signup and view all the answers

How can you determine if a relation is a function?

By checking if every vertical line intersects the graph at most once Signup and view all the answers

Which of the following statements is true about functions?

A function must be either one-to-one or many-to-one Signup and view all the answers

If a single element in the domain is associated with multiple elements in the range, what type of relation is it?

One-to-Many Relation Signup and view all the answers

What is the condition for a graph to represent a function?

Every vertical line intersects the graph at most once. Signup and view all the answers

Which of the following statements is false?

A function is a type of one-to-one function. Signup and view all the answers

What can be said about the domain and range of a many-to-one function?

Multiple elements of the domain map to the same element of the range. Signup and view all the answers

What can be concluded about a relation if every horizontal line intersects the graph at most once?

It is a one-to-one function. Signup and view all the answers

What is the key difference between a one-to-one function and a many-to-one function?

Number of outputs for each input. Signup and view all the answers