Maths for functions and graphs

In each of the following, determine whether y is a function of x where x and y
are real numbers.
1. y^2 = 4x + 1 (x≧-1/4)
When we input x, there are 2 outcomes of y
therefore, y is not a function

2 .y = 6/x-1 (x≠0)
For x=/=0, any input x can get only 1 output y,
therefore, y is a function

3. y=√x-4 (x≧4)
Since y ≧√(4-4) = 0
Therefore, it is a function

In each of the following , y is a function of x. Find the domain of each function
1. y=9x
x can be any real number

2.y=3x^2 -1
x can be any real number

3. y= √3x+6
(3x+6) > 0 => x > -2 and x can be any real number

4. y=1/4x-3
(4x-3) =/= 0 => x =/= 3/4 and x can be any real number

5.y= 1/x^2 - x - 6
x^2 =/= 0 => x=/= 0 and x can be any real number

In each of the following, y is a function of x. Find the domain of each function.
1. y = 1/√x-3
x - 3 > 0 => x > 3 and x can be any real number

2. y = 1/1+1/x
x =/= 0 and x can be any real number

3. y=√x (x+1)
x >=0 and x can be any real number