Lesson 3 – Graphs of Relations and Functions
Specific Outcomes:
Interpret and explain the relationships among, data, graphs and situations (1.1 – 1.5).
Describe and represent linear relations, using words, ordered pairs, table of values, graphs, equations (4.1 – 4.7).
Graphing:
 Plotting data on a Cartesian plane as ordered pairs.
 If the domain and range are only “elements” of the graph, then DO NOT connect the
points on the graph. This is called a discrete graph.
 If the domain and range are an element of all real numbers (Ɍ), then connect the
points and draw arrows at both ends of the line. This is called a continuous graph.
 E.g., {(1, 3), (4, 7), (12, 19)}  Do not connect the points
𝑦 = 2𝑥 − 1  Connect the points (x could represent any real number)
Example 1: Determine if the following graphs are discrete or continuous.
a)
b)
c)
Example 2: Graph the equation 𝑦 = 2𝑥 − 5 for the domain {-2, -1, 0, 1, 2}, and for the
domain of the Real numbers.
Input
Output
Ordered Pair
a) Determine the range value when the
(x, y)
x
y
domain value is 6.
b) Determine the domain value when the
range value is 3.
D: {-2, -1, 0, 1, 2}
D: Real Numbers
Example 3: Graph the equation 𝑦 = −𝑥 − 2 for the domain {-3, -1, 0, 1, 3}, and for the
domain of the Real numbers.
Input
Output
Ordered Pair
a) Determine the range value when the
(x, y)
x
y
domain value is 5.
b) Determine the domain value when the
range value is 0.
D: {-3, -1, 0, 1, 3}
D: Real Numbers
Practice Questions: Page 295 # 11, 12(a), 13(a, b), 14, 16, 17
Recall:



The set of first elements in a relation is called the domain (Independent Variable),
and it always refers to the x-coordinates of ordered pairs.
The set of second elements in a relation is called the range (Dependent Variable),
and it always refers to the y-coordinates of ordered pairs.
A function is a special type of relation where each element in the domain is
associated with exactly one element in the range. (Vertical Line Test).
Example 4: Which of these graphs represents a function? State the domain and range
of each relation that is a function (Discrete Graphs).
a)
b)
Domain/Range of Graphs with Continuous Values:
1. Set Notation:
 Use curly brackets
 Must end the domain/range with element of real numbers (ϵɌ)
2. Interval Notation:
 Use two different types of brackets: ( ) are used when endpoints are not included
[ ] are used when endpoints are included
 Use ∞ and −∞ when there are no endpoints
 Use ( ) brackets with ∞ and −∞
Example 5: State the domain and range for the following graphs in set notation and in
interval notations.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Practice Questions: Page 294 # 4, 7 – 9 (Write domain/range in set and interval notation)