Question

Determine the domain and range of F(x)=2(x+1)^2-3

Answer 1

Answer: domain: all real numbers. range: [-3, infinity)

Explanation:

We've got
`f(x) = 2(x+1)^2 - 3`.

You can plug in any number for
`x` without a problem, so the domain is all real numbers, written
`\mathbb R`.

If you graph the function, you can see it touches -3 but cannot go lower; however, it can reach anything higher than -3. Therefore the range is
`[-3, \infty)`.

Answer 2

domain is 0
range is -1