Step 1

Given:

The equation \(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}+{4}{x}-{6}{y}-{3}={0}\)

First using the software graph the function, and then by the analysis of the graph find the domain and range.

It is clear from the graph that the domain of the function is \(\displaystyle-{6}{<}{x}{<}{2}\)

and the range of the graph of a function is \(\displaystyle-{1}{<}{y}{<}{7}\)