First let's remember what is the domain and range of a function:
So the domain is all the values of x that you can give to the function, for example in the function that we have in the problem we can't use for example x=-8 because the values of x only include numbers from -6 until infinite, and the range is in the y axis what is the values you can have in this example we can't get values greater than 4 so the range is from 4 until - infinite.
Note: The circle in the point (-6,4) indicates that this point is included in the function if the point were open that means the point is not included in the function. And the arrow at the end means the function continues infinitely.
Now let's see what correct notations we can use for the domain, remember that the domain of the function is from -6 (included) until infinite, so we have to find the correct way to express that, let's write the correct options and explain why:
a) [-6,∞) is correct because includes -6 (because of the "[" ) and goes to infinity (infinity must have ")" at the end of the notation )
k) -6≤x is correct because includes -6 because of the "≤" and we can assume that goes to infinity because we don't have any other restriction
f) -6≤x<∞ is correct because includes -6 because of the "≤" and goes to infinity (in this notation we have to use "<" for infinity because we never reach infinity that's why you can't use "≤")
