Please check the expression and answer the following questions. A rational function f\left(x\right)=\frac{\left(x^{2}-3x+2\right)\cdot\left(x-3\right)}{\left(x+1\right)\cdot\left(x^{2}\ -7x\ +\ 12\right)} With the help of zeros, asymptotes, domain, and range, try to plot the function without the Desmos graph-making tool, then plot the same with the Desmos graphing tool, and check if your plot is the same as the Desmos’s plot or not. If your graph was not the same as the Desmos graphing tool, write which point you missed while plotting the graph without the Desmos graphing tool. Please provide detailed steps regarding how to plot the function above without the desmos graph.

Please check the expression and answer the following questions.

A rational function

f\left(x\right)=\frac{\left(x^{2}-3x+2\right)\cdot\left(x-3\right)}{\left(x+1\right)\cdot\left(x^{2}\ -7x\ +\ 12\right)}

With the help of zeros, asymptotes, domain, and range, try to plot the function without the Desmos graph-making tool, then plot the same with the Desmos graphing tool, and check if your plot is the same as the Desmos’s plot or not. If your graph was not the same as the Desmos graphing tool, write which point you missed while plotting the graph without the Desmos graphing tool.

Please provide detailed steps regarding how to plot the function above without the desmos graph.