Question

Answer the following question. Given: R = {(x, y): y = -x²} What is the range of R?

a) y ≥ 0

b) y ≤ 0

c) y ∈ R

d) y ≠ 0

Answer 1

In the relation R = {(x, y): y = -x²}, the range of R is all real numbers y that are less than or equal to zero.

Step-by-step explanation:

The given relation R = {(x, y): y = -x²} describes a parabola that opens downwards since the coefficient of x² is negative. This means that as x can take any real number value, y will always be less than or equal to zero because squaring any real number yields a non-negative result, and the negative sign in front of x² will make y non-positive. Therefore, the correct answer to the question 'What is the range of R?' is b) y ≤ 0.