Answer
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Shifted 2 units up. $y=x^2+2$
Final step (blue graph): Shifted 1 unit to the right. $y=(x-1)^2+2$
There are no x-intercepts.
The y-intercept is (0,3).
The domain is $(-\infty,\infty)$
The range is $[2,\infty)$
Work Step by Step
The x-intercepts are all points of a graph when f(x)=0 while the y-intercepts are all points of a graph when x=0.
The domain is a horizontal span from the function's smallest value of x to the function's largest value of x.
The range is a vertical span from the function's smallest value of f(x) to the function's largest value of f(x).