Discuss and find the Zeros and Asymptotes of the above rational function. What is the difference between zeros and asymptotes?

Question

Please check the expression and answer the following questions.

1. Discuss and find the Zeros and Asymptotes of the above rational function. What is the difference between zeros and asymptotes?
2. Discuss the Domain and range of the above rational function. Justify the reason for selecting the domain and range.

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 from your textbook (Abramson, J., 2021, Section 5.6) you missed while plotting the graph without the Desmos graphing tool. 

Answer 1

a zero is an x intercept where the graph crosses or touches the x axis

a vertical asymptote is where the graph has no x value and there is no x intercept or y intercept at that x value

the asymptote is a limit. the zero isn't

the domain includes the zero

the domain does not include the x value of the vertical asymptote

the range does not include the y value of a horizontal asymptote