So, let us disect the different options:
a) The domain is all real numbers. YES
Well, what is the domain of a function? It is the set of all the x-values, or in other words the set of all numbers I am allowed to plug in this specific function.
Now, as sqrt(18) is going to give us something between 4 and 5 (bc 4=sqrt(16)0, which means that sqrt(18)^x if defined for all real numbers, and therefore f is as well.
B) The range is y>3. NO
Well, for any exponential function g(x)=a^x for some a>0 the range is the positive real numbers. In other words every y is an element of the interval (0,infinity). The same holds for our function here. The factor 3 in the front does not change anything about our range, as we get infinitely close to zero with sqrt(18)^x for “very negative” x values, whee the factor 3 does not make a difference.
c and d) Initial value is 3 or 9. c is true
I would assume with initial value is meant the value the function f has at x=0. Well, lets plug 0 into our function and see what happens:
3*sqrt(18)^0=3*1=3
We us the fact that x^0=1
e) The simplified base is 3sqrt(2). YES
Let us inspect the base sqrt(18). Can we find the prime divisors for 18? Sure, as 2 divides 18, we get 9, which is not divisible by 2 but 3, remaining is 3. Therefore 18=2*3*3=2*(3^2)
Hence,
Sqrt(18)=sqrt(2*(3^2) )=sqrt(2)*sqrt(3^2)= sqrt(2) *3
Hope you could learn from this ;)