So for this question it says, the graph of the function f(x)= radical of x+4 is shown. The domain of the function is

1) {x|x is greater than 0}
2) {x|x is greater or equal to 0}
3) {x|x is greater than -4}
4) {x|x is greater than or equal to -4}
I know that the answer is 4 but I really don't understand how do you find the domain of this function. Will someone explain??

√u is real only for positive u.

So, that means √(x+4) is real only for positive values of x+4:

x+4 >= 0
x >= -4

To determine the domain of a function, you need to consider the possible values that x can take in order to yield real outputs. In this case, we have the function f(x) = √(x + 4).

The expression inside the square root (x + 4) must be non-negative, meaning it cannot be a negative number. If it were negative, we would be taking the square root of a negative number, which would result in an imaginary or complex number. Therefore, x + 4 must be greater than or equal to 0.

Solving this inequality, we subtract 4 from both sides of the equation:
x + 4 ≥ 0 - 4
x ≥ -4.

So, the domain of the function is all real numbers equal to or greater than -4. This corresponds to option 4) {x|x is greater than or equal to -4}.