Question

The graph of a quadratic function with vertex (-1, -3) is shown in the figure below.

Find the domain and the range.
Write your answers as inequalities, using x or y as appropriate.

Answer 1

For the given graph we have:

D: (-∞, ∞)

R: (-∞, -3]

How to find the domain and the range?

For a funcyion y = f(x), the domain is the set of possible inputs and the range is the set of possible outputs.

First for the range, this is a parabola, it extends over all the real values (we can use any real value x for the input) so the domain is:

D: R

It also can be written as:

D: (-∞, ∞)

Now the range. We can see that the parabola opens downwards, so the range will be the set of all numbers smaller than the y-value of the vertex, then we can write it as:

R: (-∞, -3]