Question

Determine whether the relation 3y - 6x^2 = 9 represents a function. If it does, state the domain and range.

a. It represents a function; Domain: all real numbers, Range: all real numbers greater than or equal to 3
b. It represents a function; Domain: all real numbers, Range: all real numbers
c. It doesn't represent a function
d. None of the above

Answer 1

The relation 3y - 6x^2 = 9 represents a function. The domain is all real numbers, and the range is all real numbers greater than or equal to 3.

Step-by-step explanation:

The relation 3y - 6x^2 = 9 may represent a function. To determine if it is a function, we rearrange the equation to solve for y:

3y = 6x^2 + 9

y = 2x^2 + 3

This equation is now in the form y = f(x), which means for each value of x, there is exactly one value of y. Hence, it represents a function. Now, let's talk about the domain and range of this function. The domain is the set of all possible inputs (x-values), and since there are no restrictions on the value of x in the equation y = 2x^2 + 3, the domain is all real numbers. The range is the set of possible outputs (y-values). Because the smallest value of y occurs when x = 0 (y = 3), and y will increase as x moves away from zero (since it is a parabola opening upwards), the range is all real numbers greater than or equal to 3.