A function is a special type of relation in which each element of the domain is paired with exactly one element in the range.
To determine which of the options are functions, we will have to check each one.
FIRST OPTION
The values of x and y are given as follows:
Since each x-value has exactly one y-value, this satisfies the condition for a function.
Therefore, THIS IS A FUNCTION.
SECOND OPTION
This is a mapping diagram. For a function, each element of the domain (x-value) is paired with exactly one element in the range (y-value).
In the mapping in the option, the domain (0) is paired with two range values (7 and 52).
Therefore, this is not a function.
THIRD OPTION
For a graph, a function occurs if there is only one y-value for each x-value. This can be checked using the vertical line test.
If a vertical line were to be drawn at x = -3, -2, 2, 3, we will see that there are multiple values for the value of x.
Therefore, this is not a function.