Cambridge International AS and A Level Mathematics Pure Mathematics 1

Functions

P1^

4

Figure 4.3 illustrates some different types of mapping. The graphs in (a) and (b)

illustrate functions, those in (c) and (d) do not.

ExERCISE  4 a   1  Describe each of the following mappings as either one-to-one, many-to-one,

one-to-many or many-to-many, and say whether it represents a function.

y

y = x  

O x

y

y = ±2x

O x

–1

1

y y = x (^3) – x
x
–1
O 1
y
–5 x
–5
5
O 5
y = ± 25 – x^2
(a) One-to-one (b) Many-to-one
(c) One-to-many (d) Many-to-many
Figure 4.3
domain: –5  x  5
(i)
(iii)  (iv)
(vi) 
(vii) 
(ii)
(v) 
(viii)