answers€¦ · 2016 mav mathematical methods trial exam 2 solutions 14 © the mathematical...
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ANSWERS
Use co-ordinate mapping rule above
3- x -2-2
Now use the co-ordinate mapping rule above:
2016 MAV Mathematical Methods Trial Exam 2 Solutions 14
© The Mathematical Association of Victoria, 2016
SECTION B EXTENDED RESPONSE QUESTIONS
Question 1 (14 marks)
a.
Substitute the point
163= a −8( )
23
163= 4a
a = 43
1M Show that
b. Shape 1A Endpoints 1A
c. reflects the graph over the y-axis.
As the function is an even function the transformation described makes no difference. 1A
d.
• a dilation of a factor of 2 units from the x-axis gives
then
• a translation of 3 units up gives 1A
23( )f x ax=
168,3
⎛ ⎞−⎜ ⎟⎝ ⎠
1( ) ( )f x f x= −234( )
3f x x=
238
3y x=
23
28( ) 33
f x x= +
2016 MAV Mathematical Methods Trial Exam 2 Solutions 15
© The Mathematical Association of Victoria, 2016
e.
• a reflection in the x-axis gives
• a reflection in the y-axis gives
• a translation of 1 unit in the positive direction of the 𝑦-axis gives
• a translation of 3 units in the positive direction of the x-axis gives
The image equation is 2A
f.
gives =
Rearrange to get
x =x1 −12
1M
Susbtitute to find the image equation for .
1M
Image equation is
Giving 1A
g. gives a dilation of a factor of 2 from y-axis and a translation of 1 unit in the positive
direction of the x-axis from the original function where the domain was .
A dilation of a factor of 2 from y-axis gives the domain .
Then a translation of 1 unit in the positive direction of the x-axis gives a domain . 1A
23
143
y x= −
( )2233
24 43 3
y x x= − − = −
23
34 13
y x= − +
( )23
44 3 13
y x= − − +
( )23
34( ) 3 13
f x x= − − +
2 2 2: ,
0x
T R R Ty
⎛ ⎞⎡ ⎤ ⎡→ =⎜ ⎟⎢ ⎥ ⎢
⎣ ⎦ ⎣⎝ ⎠13
0 12
xy
⎤ ⎡ ⎤ ⎡ ⎤+⎥ ⎢ ⎥ ⎢ ⎥− ⎣ ⎦ ⎣ ⎦⎦
20⎡⎢⎣
13
0 12
xy
⎤ ⎡ ⎤ ⎡ ⎤+⎥ ⎢ ⎥ ⎢ ⎥− ⎣ ⎦ ⎣ ⎦⎦
11
13
2 12
x xy y+⎡ ⎤ ⎡ ⎤
=⎢ ⎥ ⎢ ⎥− + ⎣ ⎦⎣ ⎦
y = y1 − 2− 13
= −3 y1 − 2( )234( )
3f x x=
−3 y1 − 2( ) = 43x1 −12
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23
23
11
14 29 2xy −⎛ ⎞= − +⎜ ⎟
⎝ ⎠234 12
9 2xy −⎛ ⎞= − ⎜ ⎟
⎝ ⎠234 12
9 2xy −⎛ ⎞= − ⎜ ⎟
⎝ ⎠234( )
3f x x= [ ]8,8−
[ ]16,16−
[ ]15,17−
2016 MAV Mathematical Methods Trial Exam 2 Solutions 16
© The Mathematical Association of Victoria, 2016
h. Shape 1A Endpoints 1A Coordinates of Cusp and
y-intercept 0, 2− 49
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1A