Which of the following could be the graph of f(x)=-a(x+b)^1/2 if both a and b are positive numbers

Option D.

Step-by-step explanation:

We have the function:

f(x) = -a*(x + b)^(1/2)

Where:

a > 0

b > 0

Now, as a is positive and we have the coefficient "-a", we will have that the function is always negative.

Why? because (x + b)^(1/2) is always positive.

then: -a*(x + b)^(1/2) is always negative.

We also should see that the domain is not the set of all real numbers, because if:

x + b < 0, then we have the square root of a negative number, and we know that this is a complex number.

The only option that meets these two conditions is option D.

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative