Gr12 Mathematics: Ch 2.1 Functions and Relations
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Questions and Answers

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?

<p>One-to-Many Relation (D)</p> Signup and view all the answers

What is the range of a function?

<p>The set of all outputs of the function. (A)</p> Signup and view all the answers

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

<p>Each element of the domain maps to a unique element of the range. (C)</p> 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?

<p>Exactly one (C)</p> Signup and view all the answers

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

<p>At least one vertical line intersects the graph more than once (B)</p> Signup and view all the answers

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

<p>A city and its population (C)</p> Signup and view all the answers

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

<p>To visualize the relationship between the domain and range (D)</p> Signup and view all the answers

How can you determine if a relation is a function?

<p>By checking if every vertical line intersects the graph at most once (B)</p> Signup and view all the answers

Which of the following statements is true about functions?

<p>A function must be either one-to-one or many-to-one (B)</p> 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?

<p>One-to-Many Relation (C)</p> Signup and view all the answers

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

<p>Every vertical line intersects the graph at most once. (C)</p> Signup and view all the answers

Which of the following statements is false?

<p>A function is a type of one-to-one function. (B)</p> Signup and view all the answers

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

<p>Multiple elements of the domain map to the same element of the range. (C)</p> Signup and view all the answers

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

<p>It is a one-to-one function. (B)</p> Signup and view all the answers

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

<p>Number of outputs for each input. (B)</p> Signup and view all the answers

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