Answer to Question #157854 in Discrete Mathematics for Annie Elijah

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 $\{1,4,9,16\}$