$1.$ True or False $(10$ pts $2$ pts each$)$

$\_\_\_$ An algorithm that runs in O$($n$)$ time will always be faster than an algorithm that runs in O$($n$2$

$)$ time.

$\_\_\_$ If an algorithm runs in $\backslash$Theta $($n$)$ time, it must also run in $\backslash$Omega $($n$)$ and O$($n$)$ time.

$\_\_\_$ It is generally simpler to derive the average$-$case runtime of an algorithm than it is to derive the

best$-$case or worst$-$case runtime.

$\_\_\_$ If an algorithm has a worst$-$case time complexity of O$($n log n$)+$ O$($n$),$ then the worst$-$case time

complexity could also be considered O$($n log n$).$

$\_\_\_$ Let f$($x$)=$ x$2$

$+2$x $+4.$ Then, f$($x$)=$ O$($x$3$

$).$