Question

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

Answer 1

graph{x^2-3 [-10, 10, -5, 5]}

Domain: (negative infinity, positive infinity)
Range: [-3, positive infinity)

Explanation:

Put two arrows on the two edges of the parabola.

Using the graph I've provided you, find the lowest x-value.
Keep going left and look for a stopping place which is not possibly the range of low x-values is infinite.
The lowest y-value is negative infinity.

Now find the highest x-value and find if the parabola stops anywhere. This can be (2,013, 45) or something like that, but for now, we like to say positive infinity to make your life easier.

The domain is made of (low x-value, high x-value), so you have (negative infinity, positive infinity)

NOTE: infinities need a soft bracket, not a brace.

Now the range is a matter of finding lowest and highest y-values.

Move your finger around the y-axis and you'll find the parabola stops at a -3 and does not go deeper. The lowest range is -3.

Now move your finger towards the positive y-values and if you'll be moving in the directions of the arrows, it's going to be positive infinity.
Since -3 is a integer, you would put a brace before the number. [-3, positive infinity).