Question

How do you graph `y=sqrtx+4`, compare it to the parent graph and what is the domain and range?

Answer 1

domain is `{x: x>=0 and x in RR}`
range is `color(white)("d."){y: y>=4 and y in RR}`
The transformation is `y=sqrt(x)` raised vertically by 4

Explanation:

You have a problem with this.

Apparently if you write `sqrt("something")` it is considered as representing the principle root. That is; the answer excludes the negative side of the squared values that will give `"something"` when squared.

So you have the general shape of `sub` but only the top half of it.

Adding 4 raises that plot up the `y` axis by 4

To avoid going into complex numbers the value being square rooted must be 0 or greater.

So we have the condition `x>=0`

Thus the domain is `{x: x>=0 and x in RR}`

When `x=0` we have `y=sqrt0+4=4`

So the range is `{y: y>=4 and y in RR}`

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Did you know that this is the same graph as:

`x=(y-4)^2 = y^2-8y+16`

That is: a quadratic in `y`