Including which of the following points in the function {(ball, circle), (kite, diamond), (stop sign, octagon)} would make it no longer be a function?
To determine if a relation is a function, we need to ensure that each input (ball, kite, stop sign) is associated with exactly one output (circle, diamond, octagon). If any input is associated with more than one output, then the relation is not a function.
Let's go through each point in the given function and check if any input is associated with multiple outputs:
1. (ball, circle): This point is fine because ball is associated with only one output (circle).
2. (kite, diamond): This point is also fine because kite is associated with only one output (diamond).
3. (stop sign, octagon): This point is also fine because the stop sign is associated with only one output (octagon).
Since none of the inputs are associated with multiple outputs, all the points in the given function satisfy the requirement for it to be a valid function.
In conclusion, including any of the given points would not make the function no longer be a function.
depends on the original sets. If it contained (ball,*),(kite,*),(stop sign,*)
where the * does not match the other corresponding outputs, it is no longer a function.