Cambridge International Mathematics

400 Introduction to functions (Chapter 19)

2 For the following graphs, determine:

i the range and domain ii whether it is the graph of a function

ab

cd

3 If f(x)=5x¡x^2 , find in simplest form:

a f(¡3) b f(¡x) c f(x+1)

4 Sketch the graph of y=g(x) where g(x)=3¡ 2 x on the domain fxj¡ 36 x 63 g.

State the range of this function.

5 For f(x)=x^2 +x¡ 2 and g(x)=2x+1, find the simplest form:

a f(g(x)) b g(g(x)) c f(g(¡2))

6 Determine the equations of the following reciprocal graphs:

ab

7 Find the function f(x)=jax+bj given:

8 By replacing jxj withxfor x> 0 and (¡x) for x< 0 , write y=jxj+4without the

modulus sign. Hence graph the function.

y

x

2

-2

-6

O

y

-4 x

x¡=-2

y=3

O

y

x

-3

O

y

x

()1 -3,

O

y

O x

()-2 -3,

x

y

O

()-4 ¡3,

O x

y

3

1

¦()x

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y:\HAESE\IGCSE01\IG01_19\400IGCSE01_19.CDR Friday, 3 October 2008 12:05:40 PM PETER