Question

Sketch each of the following domains and determine whether it is of type 1, type 2, both or neither.

(a) (x, y) such that 0≤ y3x,≤ 0 ≤ x ≤1.

(b) x, y) such that 2y2 − 1 ≤ x

(c) (x, y) such that y2 ≤ x≤ y, 0 ≤ y≤ 1

(d) (x, y) such that 1 − x2≤ 2y, x2 + y2 ≤ 1

(e) x, y) such that x2 + y2 ≤ 1.

(f) x, y) such that 1/2 x≤ 2 + y2 ≤1

Answer 1

The domains can be seen in the figures below.

(a) The domain is a triangle with vertices (0, 0), (1, 0) and (1, 3). It is a domain of both types.

(b) This domain can be written as

It is a type 2 domain, but not a type 1 domain.

(c) This domain can be written as

and hence it is a domain of both types.

(d) The domain can be written as

(e) The domain can be written as

and it is a domain of both types.

(f) This domain is neither of type 1 nor of type 2