How do you graph #y=sqrtx-2# and what is the domain and range?

Answer 1

See below.

This is how the graph appears:

sqrt(x)-2 graph{[-10, 10, -5, 5]}

The domain is all possible values of #x# that give out a defined value of #f(x)#.
Here, #y# will be undefined if #x<0#, as the square root function cannot, really, have an input below #0#
So #x>=0#.
In interval notation, the domain is #[0,oo)#.
The range is all possible outputs of #f(x)#.
Since a square root function does not give an answer above #0#, the range of #sqrt(x)# is #y>=0#. However, since the above function is #sqrt(x)-2#, the range is #y>=-2#, or in interval notation:
#[-2,oo)#.
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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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