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#.

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.
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Answer 2

Domain: x ≥ 4 Range: y ≥ 0

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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