Question

find the domain and range of the function
F(x)=(x-1)^2+1

Answer 1

would the answer be (1,1)

Answer 2

(1,1) is the vertex of the parabola not the domain and the range.

Answer 3

i thought (h,k) would be the domain and range
and in one of those equations its (x-h)^2+k

Answer 4

how would you find the domain and range then?

Answer 5

Domain means: What are the allowed values for x?
Here we see NO restrictions placed on the x value. x can be anything from -infinity to +infinity. So the domain is: (-infinity, infinity)

Range is the lowest to the highest value that y can take.
This is a parabola that opens upward which means it has a minimum at the vertex.
The vertex is (1,1) so the lowest y value is 1.
The highest y value is +infinity.
So range is: [1, infinity)
Notice on the left is a bracket '[' and not a parenthesis '('. It means 1 is included in the range.

Answer 6

i have a question how did you find out that the x value has no restrictions?