1. Grade 11 University: (MCR3U) Unit 1: Algebra & Quadratic Functions Functions & Relations: Domain and Range by Graph
Mr. Choi
© 2017 E. Choi – MCR3U - All Rights Reserved

2. Relations and Functions
Relations: Relation is a set of ordered pairs. (x, y)
Functions: A function is a special type of relation which is a set of
ordered pairs in which for every value of x, there is only
one value of y.
Independent variable: horizontal axis variables, normally x
Dependent variable: vertical axis variables, normally y
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

3. Vertical line test
If any vertical line passes through more than one point on the graph, then the relation is not a function.
Domain and Range
Domain: All possible values of ­x (independent variables); the set of the
first elements in a relation.
Range: All possible values of y (dependent variables) within the domain;
the set of second elements in a relation.
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

4. Example 1: Domain and Range with Ordered Pairs Given the relations:
a) (1,2) (3,4) (5,6) (7,8) b) (2,4) (3,5) (3,6) (4,7)
i) Graph the relations on the given grid.
ii) Determine the domain and range for the relations;
iii) Create a mapping diagram for the ordered pairs;
iv) Are they representing a function or a relation?
a) (1,2) (3,4) (5,6) (7,8)
b) (2,4) (3,5) (3,6) (4,7) 1 3 5 7 2 4 6 8 2 3 4 5 6 7
Domain:
Domain:
Function
Relation
Range:
Range:
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

5. Example 2: Domain and Range with Diagrams
Determine the domain and range for the following diagrams, are they represent a function or a relation?
Domain:
Domain:
Range:
Range:
Function
Function
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

6. Example 2: Domain and Range with Diagrams
Determine the domain and range for the following diagrams, are they represent a function or a relation?
Domain:
Domain:
Range:
Range:
Relation
Function
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

7. Example 2: Domain and Range with Diagrams
Determine the domain and range for the following diagrams, are they represent a function or a relation?
Domain:
Domain:
Range:
Range:
Relation
Function
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

8. Example 2: Domain and Range with Diagrams
Determine the domain and range for the following diagrams, are they represent a function or a relation?
Domain:
Domain:
Range:
Range:
Relation
Function
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

9. read as “Function of x” or “F of x”
Function Notations
In algebra, symbols such as x & y are used to represent numbers. To represent functions, we often use symbols such as f(x) and g(x).
For example:
read as “Function of x” or “F of x”
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

10. Example 3: Evaluating Functions Given:
Find: a) f(2) b) f(-1) c) f(0.5)
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

11. Example 4: Evaluating Function from graph From the graph of as shown:
Find: a) f(5) b) f(0) c) f(-4)
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

12. Example 5: Composition of Functions Given: Find: a) f(c) b) f(2x)
c) g( 1 𝑥 ) d) f(x – 2)
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

13. Example 5: Composition of Functions (Continued) Given:
Find: e) f(3) + g (2) f) f(g(x))
g) g(f(-2)) d) f(g(0))
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

14. Homework
Work sheet: Functions, Domain and Range by Graph (all) Factoring – Mixed Review Text: P. 12 #1-5, 7, P. 22 #1, 5, 15 Check the website for updates
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved

15. End of lesson © 2017 E. Choi – MCR3U - All Rights Reserved
Functions & Relations: Domain and Range by graph
© 2017 E. Choi – MCR3U - All Rights Reserved