Big$-$O notation. We have learnt big$-$O notation to compare the growth rates of functions, this exercise helps you to better understand its definition and properties. $($a$)(14$ points$)$ Suppose n is the input size, we have the following commonly seen functions in complexity analysis: f

$1$

$$

$($n$)=1,$f

$2$

$$

$($n$)=$logn$,$f

$3$

$$

$($n$)=$n$,$f

$4$

$$

$($n$)=$ nlogn$,$f

$5$

$$

$($n$)=$n

$2$

$,$f

$6$

$$

$($n$)=2$

n

$,$f

$7$

$$

$($n$)=$n$!,$f

$8$

$$

$($n$)=$n

n

$.$