Question

Which of the following relations are functions? Give reasons.

If it is a function determine its domain and range
(i) $\left\{\right(2,1),(5,1),(8,1),(11,1),(14,1),(17,1\left)\right\}$
(ii) $\left\{\right(2,1),(4,2),(6,3),(8,4),(10,5),(12,6),(14,7\left)\right\}$
(iii) $\left\{\right(1,3),(1,5),(2,5\left)\right\}$

Answer 1

(i) $\left\{\right(2,1),(5,1),(8,1),(11,1),(14,1),(17,1\left)\right\}$

It is a function as every input has a single output.
So, $2,5,8,11,14$ and $17$ are the elements of the domain of the given relation.
Here domain $=\{2,5,8,11,14,17\}$ and range $=\left\{1\right\}$

(ii) $\left\{\right(2,1),(4,2),(6,3),(8,4),(10,5\left)\right(12,6),(14,7\left)\right\}$
It is a function as every input has a single output.
So, $2,4,6,8,10,12$ and $14$ are the elements of the domain of the given
relation.
Here domain $=\{2,4,6,8,10,12,14\}$ and range $=\{1,2,3,4,5,6,7\}$

(iii) $\left\{\right(1,3),(1,5),(2,5\left)\right\}$
Since the element $1$ corresponds to two different images i.e., $3$ and $5$ . So, this relation is not a function.