Analysis and Approaches for IBDP Maths Ebook 2 | Page 41

(b)
2
3
(c) x � 1, x � 6
A2
A1
[1]
[2]
2
Exercise 11
1. Let
x �1
f( x)
�
( x�4)(3x� 1)
, x � 4 , 1
x � .
3
(a) Express f( x ) in partial fractions.
(b) Write down the x -intercept of f( x ).
(c) Write down the equations of the vertical asymptotes of f( x ).
[4]
[1]
[2]
3�
x
2. Let f( x)
�
2
2x
�5x� 2
, x� a,
x� b,
a� b.
(a) Write down the value of a and the value of b .
(b) Express f( x ) in partial fractions.
[2]
[4]
3. Let
2
x �x�1
f( x)
�
( x�3)( x�7)
B C
A � � x �3 x � 7
.
, x �� 3, x �� 7 . f( x ) can be expressed in the form
(a) Find the values of A , B and C .
(b) Write down the equation of the horizontal asymptote of f( x ).
[6]
[1]
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