f(x) = { (1.1,3), (.2,6.125), (-3,3/4) }
You asked:
Describe the properties of the relation: $f\left(x\right) = \left\{\left(1.1, 3\right),\left(.2, 6.125\right),\left(-3, \frac{3}{4}\right)\right\}$
MathBot Answer:
The relation $f$ is a function, because every possible input of $f$ corresponds to exactly one output.
The domain of $f$ is:\[\left\{-3, .2, 1.1\right\}\]
The range of $f$ is:\[\left\{\frac{3}{4}, 3, 6.125\right\}\]
$f$ has the following properties:\[\begin{array}{c|c|l} \textbf{Property} & \textbf{Value} & \textbf{Description} \\ \hline \text{Universal} & \text{No} &\text{For any two elements } a \text{ and } b \text{ in the domain, there exists a pair } (a,b)\text{.}\\ \hline \text{Identity} & \text{No} &\text{For each element } a \text{ in the domain, there is exactly one pair } (a,a)\text{.}\\ \hline \text{Constant} & \text{No} &\text{For each element } a \text{ in the domain, the only pair is } (a,k) \text{ for some constant } k\text{.}\\ \hline \text{Symmetric} & \text{No} &\text{For each pair } (a,b) \text{ in the relation, there exists a pair } (b,a)\text{.}\\ \hline \text{Reflexive} & \text{No} &\text{For each element } a \text{ in the domain, there exists a pair } (a,a)\text{.}\\ \hline \text{Transitive} & \text{Yes} &\text{If both } (a,b) \text{ and } (b,c) \text{ are in the relation, there exists a pair } (a,c)\text{.}\\ \hline \text{One~to~One} & \text{Yes} &\text{Both the relation and the inverse relation are functions.}\\ \end{array}\]