Question

1. Identify the domain and range.

y = –1.5x²

Answer 1

The domain is the set of acceptable values of x.

In y = -1.5 x^2, there is no value x cannot have. So, the domain is the set of Reals.

The range is the set of possible values of y.

In y = -1.5x^2 , whatever is put in for x will be squared and then multiplied by a negative contant.

So the question is, can -1.5x^2 ever be positve? If x = 0, then -1.5x^2 is 0 but not positve. And, 0 is the largest -1.5x^2 will ever be.

So, the range is the set of non-positive Real numbers. That means 0 and the negative reals.

Domain: Reals
Range: y is Real such that y ≤ 0.

Take a look at the graph:
http://www.wolframalpha.com/input/?i=y+%3D+%E2%80%931.5x%C2%B2