Complete Question
The complete question is shown on the first uploaded image  
Answer:
[S]<<KM              |  	[S]=KM                   |  [S]>>KM                     | Not true
____________  |   Half of the active  | Reaction rate is         | Increasing
 ![[E_{free}]](https://tex.z-dn.net/?f=%5BE_%7Bfree%7D%5D) is about   |    sites are filled of  |    independent of      |
 is about   |    sites are filled of  |    independent of      |  ![[E_{Total}]](https://tex.z-dn.net/?f=%5BE_%7BTotal%7D%5D) will
 will                                            
  equal to ![[E_{total}]](https://tex.z-dn.net/?f=%5BE_%7Btotal%7D%5D) . |                                 |   [S]                             | lower KM
. |                                 |   [S]                             | lower KM
 _____________________________________________|____________
 [ES] is much       |                                 | Almost all active
  lower than         |                                 | sites are filled	
 ![[E_{free}]](https://tex.z-dn.net/?f=%5BE_%7Bfree%7D%5D) |                                 |
                  |                                 |
Explanation:
Generally the combined enzyme![[ES]](https://tex.z-dn.net/?f=%5BES%5D) is mathematically represented as
 is mathematically represented as 
                    ![[ES] = \frac{[E_{total}][S]}{K_M + [S]}----(1)](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7BK_M%20%2B%20%5BS%5D%7D----%281%29)
for Michaelis-Menten equation 
Where ![[S]](https://tex.z-dn.net/?f=%5BS%5D) is the substrate concentration and
 is the substrate concentration and  is the Michaelis constant
 is the Michaelis constant 
Considering the statement ![[S] < < K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3C%20%3C%20K_M)
   Looking at the equation ![[S]](https://tex.z-dn.net/?f=%5BS%5D) is denominator so it can be ignored(it is far too small compared to
 is denominator so it can be ignored(it is far too small compared to  )  hence the above equation becomes
)  hence the above equation becomes 
                ![[ES] = \frac{[E_{total}][S]}{K_M}](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7BK_M%7D)
Since ![[S]](https://tex.z-dn.net/?f=%5BS%5D) is less than
 is less than  it means that
 it means that ![\frac{[S]}{K_M}  < < 1](https://tex.z-dn.net/?f=%5Cfrac%7B%5BS%5D%7D%7BK_M%7D%20%20%3C%20%3C%201)
so it means that ![[ES] < < [E_{total}]](https://tex.z-dn.net/?f=%5BES%5D%20%3C%20%3C%20%5BE_%7Btotal%7D%5D)
   What this means is that the  number of combined enzymes![[ES]](https://tex.z-dn.net/?f=%5BES%5D) i.e the number of occupied site is very small compared to the the total sites
 i.e the number of occupied site is very small compared to the the total sites ![[E_{total}]](https://tex.z-dn.net/?f=%5BE_%7Btotal%7D%5D) i.e the total enzymes concentration which means that the free sites [
  i.e the total enzymes concentration which means that the free sites [![E_{free}]](https://tex.z-dn.net/?f=E_%7Bfree%7D%5D) i.e the concentration of free enzymes is almost equal to
  i.e the concentration of free enzymes is almost equal to ![[E_{total}]](https://tex.z-dn.net/?f=%5BE_%7Btotal%7D%5D)
Considering the second statement
       ![[S] = K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3D%20K_M)
So  this means that equation one would now become
            ![[ES] = \frac{[E_{total}][S]}{2[S]} = \frac{[E_{total}]}{2}](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%5BS%5D%7D%7B2%5BS%5D%7D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%7D%7B2%7D)
 So this means that half of the active sites that is the total enzyme concentration are filled with S
 Considering the Third Statement 
       ![[S] >>K_M](https://tex.z-dn.net/?f=%5BS%5D%20%3E%3EK_M)
In this case the  in the denominator of equation 1 would be neglected and the equation becomes
 in the denominator of equation 1 would be neglected and the equation becomes
        ![[ES] = \frac{[E_{total}] [S]}{[S]} = [E_{total}]](https://tex.z-dn.net/?f=%5BES%5D%20%3D%20%5Cfrac%7B%5BE_%7Btotal%7D%5D%20%5BS%5D%7D%7B%5BS%5D%7D%20%3D%20%5BE_%7Btotal%7D%5D)
This means that almost all the sites are occupied with substrate 
  The rate of this reaction is mathematically defined as 
              ![v =\frac{V_{max}[S]}{K_M [S]}](https://tex.z-dn.net/?f=v%20%3D%5Cfrac%7BV_%7Bmax%7D%5BS%5D%7D%7BK_M%20%5BS%5D%7D) 
 
Where v is the rate of the reaction(also know as the velocity of the reaction at a given time t) and  is he maximum velocity of the reaction
  is he maximum velocity of the reaction
 In this case also the  at the denominator would be neglected as a result of the statement hence the equation becomes
 at the denominator would be neglected as a result of the statement hence the equation becomes 
                 ![v = \frac{V_{max}[S]}{[S]} = V_{max}](https://tex.z-dn.net/?f=v%20%3D%20%5Cfrac%7BV_%7Bmax%7D%5BS%5D%7D%7B%5BS%5D%7D%20%3D%20V_%7Bmax%7D)
 
So it means that the reaction does not depend on the concentration of substrate [S]
For the final statement(Not True ) it would match with condition that states that increasing ![[E_{total}]](https://tex.z-dn.net/?f=%5BE_%7Btotal%7D%5D) will lower
 will lower 
This is because  does not depend on enzyme concentration it is a property of a enzyme
 does not depend on enzyme concentration it is a property of a enzyme