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Functions & Inverses - Past Papers & Solutions
November 2008
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February 2011
QUESTION 5
Consider the function f ( x ) 
3
 2.
x 1
5.1
Write down the equations of the asymptotes of f.
(2)
5.2
Calculate the intercepts of the graph of f with the axes.
(3)
5.3
Sketch the graph of f on DIAGRAM SHEET 1.
(3)
5.4
Write down the range of y =  f (x).
(1)
5.5
Describe, in words, the transformation of f to g if g ( x ) 
3
 2.
x 1
(2)
[11]
QUESTION 6
A parabola f intersects the x-axis at B and C and the y-axis at E. The axis of symmetry of the
x 7
parabola has equation x  3 . The line through E and C has equation g ( x)   .
2 2
y
x
B
O
3
C
g
E
f
6.1
Show that the coordinates of C are (7 ; 0).
(1)
6.2
Calculate the x-coordinate of B.
(1)
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6.3
Determine the equation of f in the form y  a( x  p ) 2  q.
(6)
6.4
Write down the equation of the graph of h, the reflection of f in the x-axis.
(1)
6.5
Write down the maximum value of t(x) if t(x) = 1 – f(x).
(2)
6.6
Solve for x if f (x 2  2)  0.
(4)
[15]
QUESTION 7
x
1
Consider the function f ( x)    .
3
7.1
Is f an increasing or decreasing function? Give a reason for your answer.
7.2
Determine f
( x) in the form y = …
(2)
7.3
Write down the equation of the asymptote of f(x) – 5.
(1)
7.4
Describe the transformation from f to g if g ( x)  log3 x .
(2)
[7]
1
(2)
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February 2012
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November 2012
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February 2013
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November 2013
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February 2014
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November 2014
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February 2015
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November 2015
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February 2016
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November 2016
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