For the following pairs of functions, show that $1$ is $\backslash$Theta $(2)$ using the formal definition of

these terms. Remember: $\backslash$Theta $(2)$ requires you to show $\backslash$Omicron $(2)$ and $(2),$ you must clearly state the

values for n$0$ and c$,$ and you should show any work for how you derived$/$verified n$0$ and c$).$

a$.1=7$n$+2,2=$ n

Note: $1$ is the time $($or space$)$ complexity function of an algorithm you$$ve analyzed.

b$.1=$ the sum of all the numbers from $1$ to n$,2=$ n$2$

Note: $1$ is still the time $($or space$)$ complexity function of an algorithm. So $1$ could be

written as: $1=1$

$=0.$ You are not analyzing the $$algorithm to sum the numbers$.$

c$.1=$ the time complexity function of the following code:

for$($int i $=0$; i $<$ n; i$++)$ for$($int j $=0$; j $<15$; j$++)$ print$(1)$;

$2=$ n

Assume that every statement $($including print$)$ takes one unit of time, like we did in class.