The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
A) (6, 9)
B) (-8, 6)
C) (9, -6)
D) (5, -8)
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To determine which point preserves the function, we need to check if the line or relationship defined by previously existing points in the table is maintained.
In a function, for every unique x-value, there should be exactly one corresponding y-value. If any of the x-values from the new points already exist in the table with a different y-value, that would violate the definition of a function.
Here are considerations for each option:
– A) (6, 9): If 6 is not already paired with another y-value, this could be valid.
– B) (-8, 6): Similar evaluation as above.
– C) (9, -6): Check if 9 is already associated with a different y-value.
– D) (5, -8): Again, check for uniqueness of x=5 with its y-value.
Since we don’t have the actual table, we can’t make a definitive choice without knowing the existing pairs. However, if the x-value in the new pair was already in the table with a different y-value, that would invalidate it as an added point.
To conclude, the safest way to ensure to preserve the function is to choose a point where the x-value is not already in use. If none of the x-values already exist in the table, then any point can preserve the function.
If we assume none of the x-values existed in the original table, then they would all be acceptable pairs. However, ensure to check the existing pairs in your table