Is f(x) = √(x-3)^2+3 a function? If so, how do I know its domain and range?

Question

anonymous · Answer

$$f(x) = \sqrt{(x-3)^{2}+3}$$

anonymous · Answer

I don't get it D:

campbell_st · Answer

in this question the domain is all real x.  

you want to avoid negatives in the square root. But given any number squared will result in a positive answer there are no restrictions on the domain. 

the range is what output do I get from the values of x that are input

Since every input will result in a positive output and when x = 3 y = square root 3

the range is y>= square root 3

anonymous · Answer

why would y me greater than or less than root 3?

campbell_st · Answer

the smallest y value occurs when (x - 3)^2 = 0.... and this is when x =3

the output will be square root 3

anonymous · Answer

why will the output be square root of 3?

anonymous · Answer

can you show me the whole calculation?

barrycarter · Answer

http://fwd4.me/0wZ4 might help