Question

How do you find the domain and range for `y=sqrt(x-4)`?

Answer 1

By observing the graph of the function, we can see that the domain is `x>=4` and that the range is `y>=0`.

Explanation:

Here's the graph of the function we are talking about:

graph{sqrt(x-4) [-1.21, 18.79, -4.32, 5.68]}

As you can see, the graph is translated to the right 4 units. The domain describes every x-value that is being taken up by the graph. Since the lowest x-value that is included in the graph is `x=4` and the graph continues on for infinity after that, the domain will be `x>=4`.

The range will be `y>=0`. The lowest y-value is at `(4,0)`. No y-values exist below this point, and there's a good reason for it. If, for instance, you put a negative value into our function, you would get a negative number in the radical. This would create an imaginary number, which isn't a real number and can't be put on a number line. Even if it was placed on the chart, the graph wouldn't pass the horizontal line test (more than one y-value exists at an x-value)and, therefore, wouldn't be a function anymore.

https://www.livescience.com/42748-imaginary-numbers.html