# What is the domain and range of this graph?

### 2 Answers

- llafferLv 71 month ago
Domain is all possible "x" values that will result in a "y". In this curve there are two gaps. One at x = -1 (there's an open circle in the middle of the curve) and one at x = 1 where the limit as x approaches 1 from the left is ∞ and the a x approaches 1 from the right is -∞.

All other values of x result in a value for y so the domain here is:

{ x | x < -1 or -1 < x < 1 or x > 1 }

or:

{ x | x ≠ -1 and x ≠ 1 }

Both say the same thing.

Range is the list of "y" values that result from the "x" values in the domain.

The gap at x = -1 creates a gap at y = -1.

And there's the mine at y = -3 where there are no data points for a similar reason why x = 1 had a gap.

So we can write the range to be:

{ y | y < -3 or -3 < y < -1 or y > -1 }

or:

{ y | y ≠ -3 and y ≠ -1 }