Including (-4, 1) would result in a relation that is no longer a function, while including (1, -4) would not affect the function property of the relation.
How to determine which ordered pair would result in a relation that is no longer a function
To determine which ordered pair would result in a relation that is no longer a function, check if any x-values are repeated in the table.
In the given table:
x: -4, -1, 0, 3
f(x): 2, -4, -2, 16
We can see that none of the x-values are repeated. Each x-value corresponds to a unique f(x) value, which means that the relation represented in the table is a function.
Now, if we were to include the ordered pair (-4, 1) or (1, -4) in the table, we need to check if the x-value is repeated.
If we include (-4, 1), the x-value -4 is already present in the table. The x-value -4 corresponds to f(x) = 2. So, if we include (-4, 1), we would have two different y-values (1 and 2) for the same x-value (-4).
Therefore, including (-4, 1) would result in a relation that is no longer a function.
On the other hand, if we include (1, -4), the x-value 1 is not repeated in the table. The x-value 1 corresponds to f(x) = -4.
So, including (1, -4) would not result in any repetition of x-values and the relation would still be a function.
In conclusion, including (-4, 1) would result in a relation that is no longer a function, while including (1, -4) would not affect the function property of the relation.
Complete question
A function is shown in the table below. If included in the 2 points table, which ordered pair, (-4, 1) or (1, -4), would result in a relation that is no longer a function? Explain your answer. *
x: -4, -1, 0, 3
f(x):2, -4, -2, 16