functions with geogebra link

1. Functions
1

2. 2
Functions and inverse functions in real life
1.The main importantly currency conversions from AED to
USD or INR etc.
2.Also, to convert from miles to kilometers the equation that
could be use is Y=1.609x, Y is the miles and X is the
kilometers you want to convert.

3. 3
LEARNING OBJECTIVES:
We are learning to :
 To recall terms relations and functions, domain, co-domain and range
which were introduced in Class XI
 To define different types of functions namely one-one(injective),
onto(surjective) and bijective functions.
 To represent and depict different functions using arrow diagrams ,and in
graphs
 To identify and classify injective, surjective and bijective functions.
 To apply the concept of bijective function to find the inverse of a
function.
SUCCESS CRITERIA:
Student can,
 Define the terms relations and functions, domain, co-domain and
range.
 Identify one-one, onto and bijective functions.
functions
 Represent the functions using arrow diagrams and read the arrow
diagrams and Graphs also interpret the difference between different types
of functions.
 Relate the fact that the bijective functions only can be invertible.

4. Definition of a function
 A function takes an element from a set and
maps it to a UNIQUE element in another set
4

5. Function terminology5
R Zf
4.3 4
Domain Co-domain
Pre-image of 4 Image of 4.3
f maps R to Z
f(4.3)

6. More functions6
1
2
3
4
5
“a”
“bb“
“cccc”
“dd”
“e”
A string length function
A
B
C
D
F
Alice
Bob
Chris
Dave
Emma
A class grade function
Domain Co-domain
A pre-image
of 1
The image
of A

7. Even more functions7
1
2
3
4
5
“a”
“bb“
“cccc”
“dd”
“e”
Not a valid function!
Also not a valid function!
1
2
3
4
5
a
e
i
o
u
Some function…
Range

8. 8
https://www.geogebra.org/m/pXx4fSk2
Learn
Domain and Range by using
graphs

9. One-to-one functions
 A function is one-to-one if each element in the co-domain
has a unique pre-image
9
1
2
3
4
5
a
e
i
o
A one-to-one function
1
2
3
4
5
a
e
i
o
A function that is
not one-to-one

10. Onto functions
 A function is onto if each element in the co-domain is an
image of some pre-image
 If Range=co-domain then given function is onto
10
1
2
3
4
5
a
e
i
o
A function that
is not onto
1
2
3
4
a
e
i
o
u
An onto function

11. Bijections
 Consider a function that is
both one-to-one and onto:
 Such a function is a one-to-one correspondence, or a
bijection
11
1
2
3
4
a
b
c
d

12. 12
2Domain and Range Animation – GeoGebra
Domain and range also bijective by
using graph
https://www.geogebra.org/m/Haw4NXyN
https://www.ixl.com/analytics/student
s-quickview?teacherId=85380222
Group activity

13. Inverse functions13
R Rf
4.3 8.6
Let f(x) = 2*x
f-1
f(4.3)
f-1(8.6)
Then f-1(x) = x/2

14. Quick survey
 How interesting was the material in this slide set? Be
honest!
a) Wow! That was SOOOOOO cool!
b) Somewhat interesting
c) Rather boring
d) Zzzzzzzzzzz
14