Final answer:
The table cannot represent a function due to the presence of an indeterminate point (0 over 0).
However, excluding this, the remaining points follow the definition of a function where each input (x-value) is associated with only one output (y-value).
Step-by-step explanation:
To determine if the table "-3 over 9, -2 over 4, 0 over 0, -3 over -9, and -2 over -4" represents a function, we can apply the definition of a function 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.
In other words, for every x-value, there must be only one corresponding y-value.
Looking at the given table:
- -3 over 9 can be simplified to -1 over 3, which is a valid point,
- -2 over 4 simplifies to -1 over 2,
- 0 over 0 is indeterminate and cannot be a valid point in a function,
- -3 over -9 simplifies to 1 over 3,
- -2 over -4 simplifies to 1 over 2.
Because there is an indeterminate point (0 over 0), this set of points cannot represent a function in its entirety.
However, excluding the indeterminate point, the remaining points do not violate the definition of a function, as no x-value is paired with more than one y-value.