Functions – Mappings; Domain and Range Examples

Example 1 (b )(a ) y

y

x

x

2

1

0 1 2

1

0 .5

– 0 .5

– 1

– 1 .5

1 .5y f x = ( ) y g x = ( )

– 3 6 0 º 3 6 0 º– 1 8 0 º 1 8 0 º

Find the domain and range of each graph.

Example 2I

III

II

IV

V

y

y

y

y

y

x

x

x

x

x

1 2

1 2

1 2

1 2

1 2

– 2

– 2

– 2

– 2

– 2

– 1

– 1

– 1

– 1

– 1

2

2

2

2

2

1

– 1– 2

1

– 1– 2

1

– 1– 2

1

– 1– 2

1

– 1– 2

Each of the following sets represents the range of one of the functions of the graphs.

(a)

(b)

(c)

(d)

}|{ yy

}2|{ yy

}0|{ yy

}21|{ yy

Each of the following sets represents the range of one of the functions of the graphs.

A. AB. BC. CD. D

}|{ yy

}2|{ yy

}0|{ yy

}21|{ yy

I

III

II

IV

V

y

y

y

y

y

x

x

x

x

x

1 2

1 2

1 2

1 2

1 2

– 2

– 2

– 2

– 2

– 2

– 1

– 1

– 1

– 1

– 1

2

2

2

2

2

1

– 1– 2

1

– 1– 2

1

– 1– 2

1

– 1– 2

1

– 1– 2

.6)2( and ,2)1( ,4)0(

if find ,)(Given 2

TTT

a, b, ccbxaxxT

Example 4Represent the function y = 2x2 – 5, where X {–2, –1, 0, 1, 2, 3} by a mapping diagram.

(b) List the elements of the domain of this function.

(c) List the elements of the range of this function.

The diagram shows a function f, mapping members of set A to members of set B.

(a)(i) Using set notation, write down all members of the domain of f.(ii) Using set notation, write down all members of the range

of f. (iii) Write down the equation of the function f.

The equation of a function g is g(x) = x2 +1. The domain of g is .(b) Write down the range of g.

1– 12– 2– 330

1

4

9

0

4

5A B

1 6

f

}|{ xx

The mapping below is of the form f : x a × 2x + b and maps the elements of x to elements of y.

(a) (i) List the elements in the domain of f. (ii) List the elements in the range of f.

(b) Find a and b.

(c) Find the value of g.

0

– 2

1

– 1

g

– 1

– 1 .7 5

0

– 1 .5

3 0

f : x 3x − 5 is a mapping from the set S to the set T as shown below.

(a) Find the values of p and q.

(b)A function g is such that g (x) =

(i) State the domain of the function g(x).

(ii) State the range of the function g(x

S T

1

q

5

p

7

1 0

2)2(

2

x

-2

A.f : x 3x − 5 is a mapping from the set S to the set T as shown below.

B.Find the value of p.

S T

1

q

5

p

7

1 0

1. f : x 3x − 5 is a mapping from the set S to the set T as shown below. Find the value of p

-2

S T

1

q

5

p

7

1 0