Name:
Sha Tin College Mathematics Department
Key Stage 4 Core Level Course
Unit 9 Assignment: Functions
Need to Know
Types of function
Linear
f ( x)  ax  b
Quadratic
Total /67
Formulae
Need to Know
Types of function
Exponential
f ( x)  a x
f ( x)  ax 2  bx  c
or
f ( x )  a ( x  b) 2  c
Cubic
f ( x)  ax 3  bx 2  cx  d
Re ciprocal
a
f ( x) 
x
Transformations of function
f ( x)  a
a causes a vertical shift upwards
Transformations of function
f ( x  a)
a causes a horizontal shift of a to the left
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
1
A: Types of function. Domain and Range. Symmetry, period,
asymptotes, vertices, intercepts.
1. (Non calc) State the domain and range of the following relation
{(2,4), (-2,4), (6, 36)}
Domain __________________________
Range ____________________________
[2]
2. (Non calc)
f(x) = x + 1
1
2
3
Domain
Range
Complete the mapping diagram to show the range of f(x)
[2]
3. (non calc)
-2
2
3
-3
Domain
4
9
Range
Is this mapping diagram showing a function?
[1]
If so, describe the function fully.
[2]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
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4. Complete this table.
Graph sketch
Name
[17]
General Form
Domain
{x : x  R}
Range
{ y : y  R}
Quadratic
Cubic
Reciprocal
y
a
x
Exponential
Total for Section A
/24
B: Sketching Graphs
1. (Calc) Sketch the graph of y = x2 + x – 6 on the axes below. Clearly label the x
and y intercepts. Write down the coordinates of the minimum point on the curve.
Coordinates of minimum point on curve (……. , ……..)
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
[5]
3
2. (Calc) Sketch the graph of y = 2x + 3 on the axes below. Clearly label any
intercepts on the x and y axis. Draw the asymptote on the graph. Write down the
equation of the asymptote.
Equation of the asymptote is y = ………..
[4]
3. (Calc) Sketch the graph of y = x3 +x2 -3x + 4 on the axes below. Clearly label any
intercepts on the x and y axis. Write down the coordinates of any maximum and
minimum points.
Coordinates of minimum point on curve (……. , ……..)
Coordinates of maximum point on curve (……. , ……..)
[5]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
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4. Draw the graphs of y = x + 3 and y = -3x + 5 on the axes below. Write down the
coordinates of the point of intersection of the two lines.
Coordinates of points of intersection (…… , …….)
Total for Section B
[5]
/19
C: Transformations of functions.
1.(no calc)
The above function is f(x) = cos x
On the above graph sketch each of the following – and label them clearly.
(a) f(x +2)
[2]
(b) f(x) + 1
[2]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
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2.(no calc)
(a) Sketch the graph of y = x2 + 1 on the axes above
[2]
(b) Sketch the graph of y = -x2 on the same axes above
[2]
________________________________________________________________________
3. (calc)
For a particular function f(x) = (x - 4)(x + 3)
Determine the following:
(a) The coordinates of the x intercepts
( ____, ____ ) and ( ___ , ___)
[2]
(b) The coordinates of the vertex
( ___ , ___ )
[2]
(c ) The coordinates of the y intercept
( ___ , ___ )
[2]
Total for Section C
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
/14
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D: Modelling Functions.
1. Is there a relationship between the area of a house and it’s selling price?
Here is the data of twelve houses with their area in square metres an their value in
AUS $ 000
Living Area Square
m
20
16
18
64
20
17
20
17
13
15
16
24
Price Aus $ 000
165
115
145
625
185
188
193
155
153
159
150
190
a) Use your Graphical Display Calculator (GDC) to draw a suitable graph of this
data. Sketch your graph in the space below.
[4]
b) Use your GDC to test to see if there is a function that could model the data. Write
the details of the function here:
Type of function _________________________
Equation of function ______________________
[2]
c) Explain why you think that this equation is suitable to model the data.
[1]
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
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d) Use your function to predict the price of a 22 square metre house.
[1]
e) Use your function to predict the price of a 40 square metre house.
[1]
f) How reliable do you think that your answers to d) and e) are?
[1]
Total for Section D
/10
Unit 9 Assignment: Functions
CAN DO STATEMENTS
Syllabus
Main Learning Objectives
Tick
Reference
Here!!
3.1
NEW Understand the meaning of domain and range and be able
to illustrate these with the use of arrow diagrams (mappings)
3.2 3.5
NEW Sketch various graphs as above in order to solve word
3.7 3.6
problems
Paper 3
NEW Understand the concept of asymptotes and identify
3.6
simple examples parallel to the axes
3.6
NEW Use a GDC to sketch the graph of a function, produce a
table of values, find zeros, local maxima or minima and find the
intersection of the graphs of functions.
Paper 3
Modelling – drawing a graph and finding a model.
Interpolating and extrapolating. Evaluating the model.
3.3 3.9
NEW Transformations of these functions. Describe and
identify, using the language of transformations, the changes to
the graph of y = f(x) when y = f(x) + k and y = f (x+k) – where
k is an integer
Paper 3
Modelling – modeling “real life” data by an appropriate
graph to find a model. Interpolating and extrapolating.
Evaluating the model.
Sha Tin College Mathematics Department KS 4 ASSIGNMENT Functions
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