Lesson 1 – Representing Relations
Specific Outcome:
- Determine, and express in a variety of ways, the domain and range of a table of values (1.5)
- Demonstrate an understanding of relations and functions (2.1 – 2.4).
- Identify independent and dependent variables in a given context (4.1).
- Represent a linear function, using function notation (8.1 – 8.5).
Cartesian Plane:
Note: Coordinates (points) are written as ordered pairs, such as (x, y).
Example 1: Write the ordered pair for each point on the graph.
Definitions:
Set: A collection of distinct objects.
Element: One object in the set. E.g., {1, 2, 3, 4, 5}
Relation:
-
A rule that associates the elements of one set with the elements of another set.
E.g., the speed of a car and the amount of time a trip will take.
It can be represented in words, ordered pairs, table of values, arrow diagrams,
equations, and/or graphs.
Example 2: Fruits can be associated with their colours. Consider the relation
represented by this table.
Fruit
Apple
Apple
Blueberry
Cherry
Huckleberry
Colour
Red
Green
Blue
Red
Blue
b) Represent this relation:
As a set of ordered pairs
a) Describe this relation in words.
As an arrow diagram
Example 3: Animals can be associated with the classes they are in.
Animal
Ant
Eagle
Snake
Turtle
Whale
Class
Insect
Aves
Reptile
Reptile
Mammal
b) Represent this relation:
As a set of ordered pairs
a) Describe this relation in words.
As an arrow diagram
Example 4: Different breeds of dogs can be associated with their mean heights.
Consider the relation represented by this graph. Represent the relation:
a) As a table
b) As an arrow diagram
Practice Questions: Page 262 # 3, 4
Properties of Functions:
 The set of first elements in a relation is called the domain (Independent Variable).
 The set of second elements in a relation is called the range (Dependent Variable).
 A function is a special type of relation where each element in the domain is
associated with exactly one element in the range.
Relation Versus Function:



A relation produces one or more output numbers for every input number.
A function produces exactly one output number for every input number.
In order to determine if a graph is a function, we can use the “vertical Line Test”.
This means if we draw a vertical line anywhere on the graph, and two or more points
on the graph lies on the line, then the graph is not a function.
Example 5: Determine if the following are functions.
a) {(-1, 2), (5, 8), (5, 13)}
b)
c)
d)
Example 6: For each relation below,
 Determine whether the relation is a function.
 State the domain and range.
a) Cost of berries in a grocery store.
{(blueberries, $2.99), (strawberries, $4.99), (blackberries, $2.99), (raspberries, $3.99)}
b)
Example 7: For each of the following relations,



Identify if the relation is a function, and justify your answer.
Identify the independent variable and dependent variable. Justify the choices.
State the domain and range.
a) The table shows the masses, m grams, of different numbers of identical marbles, n.
b) The table shows the costs of student bus tickets, C dollars, for different numbers of
tickets, n.
Example 8: The equation V = -0.08d + 50 represents the volume, V litres, of gas
remaining in a vehicle’s tank after travelling d kilometres. The gas tank is not refilled
until it is empty.
a) Describe the function. Write the equation in function notation.
b) Determine the value of V(600). What does this number represent?
c) Determine the value of d when V(d) = 26. What does this number represent?
Example 9: The equation C = 25n + 1000 represents the cost, C dollars, for a feast
following an Arctic sports competition, where n is the number of people attending.
a) Describe the function. Write the equation in function notation.
b) Determine the value of C(100). What does this number represent?
c) Determine the value of n when C(n) = 5000. What does this number represent?
Practice Questions: Page 270 # 4, 5, 8, 9, 14 – 16