Question

find the domain and range of y=x^2 -2x +3

Answer 1

Since we can plug in ANY number into x, this means that the domain is the set of real numbers. In interval notation, the domain is \[(-\infty,\infty)\]

If you graph, or find the vertex, you'll see that the lowest point is at (1,2). So this means that the lowest y value is y = 2. So the range is the set of numbers that are greater or equal to 2. In interval notation, the range is \[[2,\infty)\]

Answer 2

The domain is R, as x can be any real number.

If you complete the square (i think it's called) you get:
\[(x-1)^2+2\]
From here you can see the range (y-values) are:
\[[2,\ \infty)\]
as
\[(x-1)^2\geq 0\ for\ all\ x\]

Answer 3

thx