Final answer:
Option c) (7,19) will create a system that is not a function when added to the given set of data points because it has the same x value as an existing point, violating the definition of a function where each x value can have only one corresponding y value.
Step-by-step explanation:
The question asks us to determine which of the following points will create a system that is not a function when added to the set of data points on the x-y grid (3,5);(4,6);(7,8); and (9,2). In mathematics, a function is defined as a relation where every input (x value) has exactly one output (y value). Therefore, for a set of points to represent a function, each x value must be unique.
Now let's examine the given points to see which one would cause the set not to represent a function:
- a) (1,2) - This has a unique x value and will not violate the function definition.
- b) (0,0) - This also has a unique x value and will not violate the function definition.
- c) (7,19) - This point has the same x value as one of the existing data points (7,8), which would mean two different y values for the same x value, thus making the set not to represent a function.
- d) (2,3) - This point has a unique x value and will not violate the function definition.
Therefore, the answer is c) (7,19), as this point would result in the set not representing a function.