Question

Find the domain and range of the ff.
1.y=√x+3
2.y=3x-5
3.y=x+1
4.y=x+3|x-2
5.y=x-6|x-7

Answer 1

#1. I assume you mean √(x+3). Since the domain of √x is x≥0, the domain here is x+3≥0 -- that is x≥-3
#2,3: the domain of all polynomials is all real numbers
#4,5: all reals except where the denominator is zero.

Answer 2

I will assume that for 4. and 5. you have a division.
The standard way to show division is / if you don't have ÷

I will also assume that you were sloppy with brackets, thus changing the meaning of the question.

4. y = (x+3)/(x-2)
domain: all real x's except x = 2,
range: all real y's except y = 1
(y = 1 is a horizontal asymptote, x = 2 is a vertical asymptote)

#5, the same type as #4

#1, y = √x + 3
domain: x ≥ 0
range : y ≥ 3
(unless you meant y = √(x+3) , again those nasty brackets! )

#2 and #3, they are both straight lines, slope ≠ 0 or undefined,
so anything goes