To identify the type of variation represented in the table, we need to observe the relationship between the values of x and y. In this table, as x doubles, y is halved.
This type of variation is called inverse variation, also known as inverse proportion or inversely proportional relationship. In inverse variation, as one variable increases, the other variable decreases in inverse proportion.
To find the y-value when x = 32, we can use the inverse variation relationship observed in the table. As x doubles, y is halved. Starting with an x-value of 2, we can see that when x doubles successively (2, 4, 8, 16, 32), y is halved each time (4, 2, 1, 0.5, ?).
Therefore, when x = 32, y would be half of the previous value, which is 0.5. Therefore, the y-value when x = 32 is 0.5.