Answer:
[tex]{(0, 3), (1, 6), (2, 9)}[/tex]
Step-by-step explanation:
we have
[tex]y-3=3x[/tex]
we know that
If the set represents possible inputs and outputs of the function, then all ordered pairs of the set must be satisfy the function
Let's verify all the cases to determine the solution to the problem
case A) [tex]{(0, 3), (1, 6), (2, 9)}[/tex]
Verify first pair
[tex](3)-3=3*(0)[/tex]
[tex]0=0[/tex] ------> is true
Verify second pair
[tex](6)-3=3*(1)[/tex]
[tex]3=3[/tex] ------> is true
Verify third pair
[tex](9)-3=3*(2)[/tex]
[tex]6=6[/tex] ------> is true
therefore
The set [tex]{(0, 3), (1, 6), (2, 9)}[/tex] represent possible inputs and outputs of the function
case B) [tex]{(3, 0), (6, 1), (9, 2)}[/tex]
Verify first pair
[tex](0)-3=3*(3)[/tex]
[tex]-3=9[/tex] ------> is not true
it is not necessary to verify the other pairs, because the first one does not meet the requirements.
therefore
The set [tex]{(3, 0), (6, 1), (9, 2)}[/tex] does not represent possible inputs and outputs of the function
case C) [tex]{(1, 3), (2, 6), (3, 9)}[/tex]
Verify first pair
[tex](3)-3=3*(1)[/tex]
[tex]0=3[/tex] ------> is not true
it is not necessary to verify the other pairs, because the first one does not meet the requirements.
therefore
The set [tex]{(1, 3), (2, 6), (3, 9)}[/tex] does not represent possible inputs and outputs of the function
case D) [tex]{(3, 1), (6, 2), (9, 3)}[/tex]
Verify first pair
[tex](1)-3=3*(3)[/tex]
[tex]-2=9[/tex] ------> is not true
it is not necessary to verify the other pairs, because the first one does not meet the requirements.
therefore
The set[tex]{(3, 1), (6, 2), (9, 3)}[/tex] does not represent possible inputs and outputs of the function
