we have
[tex]y=x^{2}-6x+1[/tex]
this is the equation of a vertical parabola open upward
Convert into vertex form
[tex]y-1=x^{2}-6x[/tex]
[tex]y-1+9=x^{2}-6x+9[/tex]
[tex]y+8=(x-3)^{2}[/tex]
[tex]y=(x-3)^{2}-8[/tex]
The vertex is the point [tex](3,-8)[/tex] ----> is a minimum
The range of the function is the interval--------> [-8,∞)
that means------> all real numbers greater than or equal to [tex]-8[/tex]
The domain of the function is the interval-----> (-∞,∞)
that means------> all real numbers
therefore
the answer is the option
All real numbers
see the attached figure to better understand the problem
