Question

How do you find the domain and range of `y=-2(x+1)^2-3`?

Answer 1

Domain: all reals
Range: `y< -3`

Explanation:

When attempting to find the domain and range, it is best if you actually draw the diagram so you don't miss any points and when you are unsure. If you don't know what the graph looks like, just plot a bunch of points. But looking at the equation `-2(x+1)^2-3` we can tell that it is an upside down parabola shifted to the left by 1 and down by 3. Its vertex will `(-1,-3)`

graph{-2(x+1)^2-3 [-10, 10, -5, 5]}

So looking at the graph,
Domain: all reals
Range: `y< -3`