Cambridge International Mathematics

2 The graph alongside has the form

y=x^3 +6x^2 +cx+d.

Find the values ofcandd.

3 Find f¡^1 (x) for:

a f(x)=8x b f(x)=

2

x¡ 1

c f(x)=

p

x+3

4 Which of the following functions have an inverse function?

abc

5 For f(x)=

x¡ 3

x^2 +3x¡ 4

:

a Use a graphics calculator to help graph the function.

b State the equations of any asymptotes.

c Find the axes intercepts.

d Find and classify any turning points.

6 Solve forx, correct to 3 significant figures:

a 3 x=11 b x^3 ¡ 6 x=5+x^2 c 5 x=x^2 +2

7 Find the coordinates of the points of intersection for:

a y=x^3 and y=

5

x

¡ 2 b y=3x+2and y=

1

x^2

x f(x) g(x)

¡ 10 0 : 833 1 : 25

¡ 5

0

5

10

15

20

8 Suppose f(x)=(1:2)

x

(^10) and g(x)=(0:8)
x
10
a Copy and complete the table of values alongside.
b For the domain given ina, write down the largest and smallest
values of f(x) and g(x).
c Use technology and partsaandbto sketch y=f(x) and
y=g(x) on the same set of axes.
d Find the point of intersection of f(x) and g(x).
e Find a linear function which:
² passes through the point of intersection off(x)and g(x)
² has a negative gradient
² does not meet either graph again in the given domain.
9 Find as accurately as possible, the gradient of the tangent to y=x^3 at the point(1,1).
-2
-10
y
x
O
y
x
O
y
x
O
y
x
O
482 Further functions (Chapter 23)
IGCSE01
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Y:\HAESE\IGCSE01\IG01_23\482IGCSE01_23.CDR Monday, 27 October 2008 2:19:02 PM PETER