Question

Determine if the following statement is true or false. The relation y = x2 - 2 defines y as a function of x.

A. False, because each member of the domain corresponds to exactly one member of the range for the given equation.
B. True, because each member of the domain does not correspond to exactly one member of the range for the given equation. For example x = 0 corresponds to two y-values, 2 and -2.
C. True, because each member of the domain corresponds to exactly one member of the range for the given equation.
D. False, because each member of the domain does not correspond to exactly one member of the range for the given equation. For example x = 0 corresponds to two y-values, 2 and -2.

Answer 1

The correct answer to whether the relation y = x^2 - 2 defines y as a function of x is true; for each x-value in the domain, there is exactly one corresponding y-value in the range.

Step-by-step explanation:

The statement 'The relation y = x2 - 2 defines y as a function of x' is true, because for each value of the domain (x), there corresponds exactly one value in the range (y). When we look at a specific example such as x = 0, plugging it into the equation y = x2 - 2 gives us y = 02 - 2, which simplifies to y = -2. There is only one y-value for this x-value, not two as the incorrect choice suggests. Therefore, the correct answer is C, because each member of the domain corresponds to exactly one member of the range for the given equation.