Question

What is the domain and range of `y+2 = (x-3)^2`?

Answer 1

Domain: `x inRR`
Range: `y in [-2,oo)`

Explanation:

The function you provided is almost in vertex form of a quadratic function, which helps greatly when answering your question. Vertex form in a quadratic is when the function is written in the following form:

`y=a(x-h)^2+k`

To write your function in vertex form, I'll simply solve for `y` by subtracting 2 from both sides:

`y=(x-3)^2-2`

The two parameters you want in this are `a` and `k`, since those will actually tell you the range. Since any value of `x` can be used in this function, the domain is:

`x inRR`

Now we need the range. As stated before, it comes from the values of `a` and `k`. If `a` is negative, the range goes to`-oo`. If `a` is positive, the range goes to `oo`. In this case, `a` is positive, so we know the range goes to `oo`. The lowest value will be the `k` value, which in this case is -2. Hence, the range of your function is:

`y in [-2,oo)`