Question

How do you find the domain and range of `y=x^2+1`?

Answer 1

Domain: `x in RR or x| (-oo,oo)`
Range : `y>= 1 or y| [1,oo)`.

Explanation:

`y=x^2+1` , Domain : Possible input value of `x` is

any real value . Therefore Domain: `x in RR or x| (-oo,oo)`.

Range: `y=x^2+1 or y = (x-0)^2+1` . Comparing with vertex

form of equation `f(x) = a(x-h)^2+k ; (h,k)` being vertex

we find here `h=0 , k=1,a=1 :.` Vertex is at `(0,1)`

Since `a` is positive the parabola opens upward and

vertex is the minimum point `x=0, y=1`

So range is `y>=1 or y| [1,oo)`.

Domain: `x in RR or x| (-oo,oo)`

Range : `y>= 1 or y| [1,oo)`.

graph{x^2+1 [-10, 10, -5, 5]}