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

1 Answer
Jun 23, 2018

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


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.