1. 1
Ago 27­06:48 p.m.
Interval notation
Starter:

2. 2
Ago 27­06:48 p.m.

3. 3
Ago 27­06:48 p.m.
By the end of the lesson you will be able to:
• Distinguish between relations and functions.
• Recognise the domain and range of a function
from its graph or/and its formula.
• Use GDC to draw graphs of functions.
• Manipulate function notation.

4. 4
Ago 27­06:48 p.m.
Relations
A relation is any set of points on the cartesian plane.
A relation is often expressed as an equation
connecting two variables .

5. 5
Ago 27­06:48 p.m.
The length side of a square is x.
Write the area of the square, A, in terms of x.
A group of friends rents a car for their holidays.
They have to pay a fixed cost of 350$ plus $120 per day.
Let C be the cost of renting the car and d the number of days the car is
rented. Write C in terms of d.
The value of a car depreciates in such a way that when it is t years old,
its value V is given by V=12000e­0.6t
.
(a) Find the value of the car after 4 years.
(b) How long does it take for the car to be worth 6000?
A(x) = x2
C(d) = 350+120d

6. 6
Ago 27­06:48 p.m.
A(x) = x2
C(d) = 350+120d V(t) =12000e­0.6t
A function is a relation in which to each value of x
corresponds one and only one value of y.
Functions
A(x) = x2 independent variable?
dependent variable?
C(d) = 350+120d
independent variable?
independent variable?
V(t) =12000e­0.6t
dependent variable?
dependent variable?

7. 7
Ago 27­06:48 p.m.
A(x) = x2
V(t) =12000e­0.6t
Function notation
Find A(3)
Find x if A(x) = 100
What is the meaning of V(4) ?
What is the image of t=4 ?

8. 8
Ago 27­06:48 p.m.
Functions can also be given by graphs
not a function
not a function
Which of these graphs represent functions?
function
function
function
vertical line test.exe

9. 9
Ago 27­06:48 p.m.
functio function
function for all real numbers
but zero
function
http://www.univie.ac.at/future.media/moe/tests/fun1/grongr.html

10. 10
Ago 27­06:48 p.m.
The domain of a function is the set of permissible
values that x may have.
A(x) = x2
Domain=
Use your GDC to plot the graph of A.
Range =
The range of a function is the set of
all the images( y ).

11. 11
Ago 27­06:48 p.m.
The domain of a function is the set of permissible
values that x may have.
The range of a function is the set of all the images( y ).
domain
range

12. 12
Ago 27­06:48 p.m.
State the domain and range of the function :

13. 13
Ago 27­06:48 p.m.
State the domain and range of the function :

14. 14
Ago 27­06:48 p.m.
State the domain and range of the function :

15. 15
Ago 27­06:48 p.m.
State the domain and range of the function :

16. 16
Ago 27­06:48 p.m.
State the domain and range of the function :

17. 17
Ago 27­06:48 p.m.
y = x2
­ 3x + 5
y = 3x + 5 y = x5
­ 3x3
Polynomial functions.
The domain of any polynomial function is the set of real
numbers:

18. 18
Ago 27­06:48 p.m.
State the domain of the function :
Draw the graph of this function with your GDC.
Is there any value of x for which you can't calculate the
value of y ?
Domain:

19. 19
Ago 27­06:48 p.m.
What is the range of this function?

20. 20
Ago 27­06:48 p.m.
State the domain of the function:
Draw the graph of this function with your GDC.
Domain:
Is there any value of x for which you can't calculate the
value of y ?

21. 21
Ago 27­06:48 p.m.
This function is called the reciprocal function.
It's graph is a hyperbola.
What is the range of this function?

22. 22
Ago 27­06:48 p.m.
Find the domain and range of:
Domain:
Draw the graph of this function with your GDC.
Is there any value of x for which you can't calculate the
value of y ?

23. 23
Ago 27­06:48 p.m.
What is the range of this function?

24. 24
Ago 27­06:48 p.m.
C
Which graph is
not a function?
y
x
x
y
x
y
x
y
D
x
y

25. 25
Ago 27­06:48 p.m.
A
B
C
D
Which graph is
a function?
A
B
C
D

26. Attachments
vertical line test.exe