Question

Construct two different assignments that are functions. The functions should be represented by means of ordered pairs graphically.

Construct domain, codomain and range(image) of each function.

Answer 1

(1) Let $A=\{1,2,3,4\}$ and $B=\{0,3,6,8,12,15\}$. Let $f:A \to B|f(x)=x^2-1,x\in A$. $f$ is an example of a function with the ordered pairs as follows; $(1,0),(2,3),(3,8),(4,15)$.

The Domain is the entire set $A=\{1,2,3,4\}$, the Co-domain is the entire set $B=\{0,3,6,8,12,15\}$ and the range of the function is $\{0,3,8,15\}$.

(2) Let $A=\{1,2,3,4,\}$ and $\R$ be the set of real numbers. Let $f:A\to \R|f(a)=a^2,a\in A$ . This function is written as ordered pairs as follows; $(1,1),(2,4),(3,9),(4,16).$

The Domain is the entire set $A=\{1,2,3,4\}$, while the Co-domain is the set $\R$ and this makes the function a real-valued function. The Range of the function is $\{1,4,9,16\}$