Final answer:
The relation y² = 36 is not a function because it fails the vertical line test, yielding two y-values (6 and -6) for the common x-value of 36. Consequently, y = ±6 is also not a function.
Step-by-step explanation:
In mathematics, a function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output. To determine whether a given relation is a function, we can apply the vertical line test. This involves sketching the graph of the relation and seeing if any vertical line would intersect the graph more than once.
When considering the statement y² = x, we notice that for a given x-value, there could be two possible y-values. For example, if x = 36, then y² = 36, which leads to two possible solutions for y: y = 6 or y = -6. Thus, when we graph these points, we observe two distinct points on the graph for x = 36: (36, 6) and (36, -6).
Answering the original question, we see that b) y² = 36 is not a function because for the x-value of 36, there are two possible y-values. Although we have two ordered pairs, the relation fails the vertical line test because a vertical line drawn at x = 36 would intersect the graph at both (36, 6) and (36, -6). Therefore, c) y = ±6 is not a function for the same reason; it represents the two possibilities of y for a given x-value when taking the square root of both sides of the original equation y² = x.