Question

what is range and domain of the relationR= {(x, y): y≥ x²– 2 and y≤2

Answer 1

Since we have that y ≤ 2, the maximum value y can have is 2, so we have that:

$\begin{gathered} 2\ge x^2-2 \\ x^2\le4 \\ |x|\le2 \\ -2\le x\le2 \end{gathered}$

So the domain of the relation is D = [-2, 2].

The range is all y values the function can have.

Since the smallest value x² can have is 0, we have that:

$\begin{gathered} y\ge0-2 \\ y\ge-2 \end{gathered}$

So we have that y ≤ 2 and y ≥ -2, therefore the range of the relation is R = [-2, 2].