y= x^2

The domain is all real numbers such that:

x = (-inf, inf) 

Now to notice that y is a positive number . Then the ramge is:

y= [ 0, +inf)

y = sqrt(1-x^2)

The domain is all x values such that 1- x^2 >= 0

==> -x^2 > = -1

==> x^2 = < 1

==>  x =< 1   and    x >= -1

==>the somain is [ -1, 1]

The range is : ( 0, 1]

y= sqrtx

x >= 0 ==> the domain is  [ 0, inf)

==>The range is :  y= [ 0, inf)

y= sqrt(4-x)

The domain is 4-x > = 0

==> 4 > = x

==> x =< 4

Then the domain is ( -inf, 4]

Then the range will be [ 0, inf)

First, let me tell you that you can only post one question at a time. I will answer your questions this time, but keep this in mind the next time you post a question here.

For a function y = f(x), all the values that x can take form the domain and all the values y can take form the range.

Here, I have assumed that y and x can only take on real values.

For y = x^2, the domain is –inf =0.

For y = sqrt (1 – x^2), the domain is 1

For y = 1/x, the domain is all values except x = 0, and the range is all values except y =0.

For y = sqrt(x), the domain is 0

For y = sqrt (4-x), the domain is x