Verified answer

Yes, y is certainly a function of x here. You need to put a real number in for x and you (sometimes) get output for y.

You need to better define your problem, however.

I don't know if the equation is

y = (√8)x+7 or

y = √(8x)+7 or

y = √(8x+7)

If it's the first one, then the domain is all real numbers and the range is all real numbers. x can be anything. y will eventually be anything.

If it's the second one, then the domain is all positive real numbers (plus zero (zero isn't considered to be positive or negative, but it is a part of the domain, so you should specifically include it)). Remember, that, for real numbers, you cannot have a negative under the radical. The range, then, will be all real numbers greater than or equal to 7. Since the lowest value of x is 0, the value of y at that point is 7. x can only increase from there. It's the same story with y.

Finally, if it's the last one, find x such that 8x + 7 >= 0. (">=" means "greater than or equal to".) You should be able to deduce that x >= -7/8, so the Domain is all real numbers greater than or equal to -7/8. The Range will be all real numbers greater than or equal to 0. As before, the Range bottoms out at zero and goes up up up to positive infinity.