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

1 Answer
Tony B
Jan 26, 2018

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}

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Did you know that this is the same graph as:

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

That is: a quadratic in y

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