Answer:
To determine if the given relation is a function, we need to check if there is a unique y-value for every x-value in the relation.
The given relation is:
y^2 + 4 = x
To test for functionality, we need to solve for y in terms of x:
y^2 = x - 4
y = ± √(x - 4)
Notice that for each x-value, there are two possible y-values, one positive and one negative. This means that for a single x-value, there are two potential y-values, violating the condition of a unique y-value for every x-value.
Therefore, the given relation is not a function since it fails the vertical line test, as there are x-values with multiple corresponding y-values.