$(8)$ Question: $(20$ points$)$ Question $3$For each group of functions, sort the functions in increasing order of asymptotic $($big$-$O$)$complexity$,$ and explain your answer.Note: "increasing order" refers to arranging the functions...

$(20$ points$)$ Question $3$

For each group of functions, sort the functions in increasing order of asymptotic $($big $-$ O$)$ complexity, and explain your answer.

Note: "increasing order" refers to arranging the functions from the one that grows at the slowest rate to the one that grows at the fastest rate. In other words, it means placing the functions in ascending order based on how quickly their time complexity increases as the input size grows.