College Math CLEP Prep Practice Exam

An inverse variation is described by the equation y = x^2/3. Which of the following would be true for the variation?

1. As y increases, x decreases

2. As y decreases, x increases

3. As y decreases, x decreases

4. As y increases, x increases

The correct answer is: As y increases, x increases

An inverse variation is a relationship between two variables where one variable increases while the other decreases at a constant rate. In the given equation, y is inversely proportional to x, which means that as one variable increases, the other decreases. The exponent of 2/3 indicates that the decrease in y will be greater than the increase in x. Therefore, as y increases, x will also increase but at a slower rate. This makes option D the correct choice. The other options are incorrect because they do not follow the pattern of an inverse variation. Option A suggests that y and x both decrease, while option B suggests that y and x both increase, which goes against the concept of inverse variation. Option C suggests that both y and x decrease, which is not consistent with the given equation.