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Functions & Inverses - Past Papers & Solutions
November 2008
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February 2010
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February 2011
QUESTION 5
Consider the function .21
3
xxf )(
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 = ).(xf (1)
5.5 Describe, in words, the transformation of f to g if .21
3
xxg )(
(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
parabola has equation 3x . The line through E and C has equation 2
7
2)(
xxg .
x
y
f
g
3
6.1 Show that the coordinates of C are (7 ; 0). (1)
6.2 Calculate the x-coordinate of B. (1)
B C
E
O
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6.3 Determine the equation of f in the form .qpxay 2)( (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 .022 )(xf (4)
[15]
QUESTION 7
Consider the function x
xf
3
1)( .
7.1 Is f an increasing or decreasing function? Give a reason for your answer. (2)
7.2 Determine )(1 xf 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 xxg 3log)( . (2) [7]
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