Question

What is the domain and range for y=sqrt(x-4)?

Answer 1

Domain: set of all numbers that can be inputted into a function

Since you cannot take the square root of a negative number, this means that x-4 CANNOT be negative. So it's either 0 or it's positive.
So.. x−4≥0
x−4+4≥0+4
x≥4

So this says: "Any number greater than or equal to 4 will result in x-4 being either 0 or some positive number"
So this means that the domain is

{x|x≥4}

This basically says: "the domain is the set of all numbers x such that x is greater than or equal to 4"

In interval notation, the domain is [4,∞)


The range is the set of all possible outputs. We can find the most extreme point of the range by plugging in the most extreme value for the domain
sqrt(x-4) = sqrt(4-4) = sqrt(0) = 0

So the smallest possible output is y=0, which means that the range is
{y|y≥0}

This basically says: "the range is the set of all numbers y such that y is greater than or equal to 0"

In interval notation, the range is

[0,∞)