For the functions, f$\_$i:$\backslash$mathbb$\{$Z$^+\}\backslash$to$\backslash$mathbb$\{$R$^+\},$ complete the chart below by selecting true if f$\_$i has the specified asymptotic bound and false, if it does not.

f$\_1\backslash$left$($n$\backslash$right$)=3($n $+1)^2$ f$\_2\backslash$left$($n$\backslash$right$)=2^\{100\}$ f$\_3\backslash$left$($n$\backslash$right$)=2^\{\backslash$lg n$\}$ f$\_4\backslash$left$($n$\backslash$right$)=\backslash$sqrt$\{7$n$^3+4$n $+1\}$ f$\_5\backslash$left$($n$\backslash$right$)=6$n$\backslash$log$\backslash$left$($n$^2+4$n $-5\backslash$right$)^3$

Asymptotic Bounds of Functions

f$\_1$ f$\_2$ f$\_3$ f$\_4$ f$\_5$

$\{\backslash$rm o$\}($n$\backslash$lg n$)$ Answer $1$ Question $1$

false

Answer $2$ Question $1$

true

Answer $3$ Question $1$

true

Answer $4$ Question $1$

false

Answer $5$ Question $1$

false

$\{\backslash$rm O$\}($n$\backslash$lg n$)$ Answer $6$ Question $1$

false

Answer $7$ Question $1$

true

Answer $8$ Question $1$

true

Answer $9$ Question $1$

false

Answer $10$ Question $1$

false

$\{\backslash$rm $\backslash$Theta$\}($n$\backslash$lg n$)$ Answer $11$ Question $1$

false

Answer $12$ Question $1$

false

Answer $13$ Question $1$

false

Answer $14$ Question $1$

false

Answer $15$ Question $1$

false

$\{\backslash$rm $\backslash$Omega$\}($n$\backslash$lg n$)$ Answer $16$ Question $1$

false

Answer $17$ Question $1$

false

Answer $18$ Question $1$

false

Answer $19$ Question $1$

false

Answer $20$ Question $1$

false

$\{\backslash$rm $\backslash$omega$\}($n$\backslash$lg n$)$ Answer $21$ Question $1$

true

Answer $22$ Question $1$

false

Answer $23$ Question $1$

false

Answer $24$ Question $1$

true

Answer $25$ Question $1$

true