SOLUTION: HOW TO DETERMINE THE domain and range for these? {(x,y,) | y= -⎷ x+3 } y= |x^2 -3x +2| +1

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Question 890578: HOW TO DETERMINE THE domain and range for these?
{(x,y,) | y= -⎷ x+3 }
y= |x^2 -3x +2| +1
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Not sure what is the first equation or how you mean; but the second equation can accept all real numbers for x, and you want to check inside the absolute value part to see if any zeros.

x%5E2-3x%2B2
%28x-1%29%28x-2%29
Vertex minimum between the two roots, at 3%2F2.
The value will be a minimum at x=3%2F2.
%283%2F2%29%5E2-3%283%2F2%29%2B2
9%2F4-9%2F2%2B2
9%2F4-18%2F4%2B8%2F4
-1%2F4, a minimum but because of absolute value, the smallest value of y will be y=1%2F4%2B1=1%261%2F4.

RANGE for y is y%3E=1%261%2F4.
Domain for y is all real numbers.