Answer:
The third set is the correct option.
Step-by-step explanation:
We have the following function :
[tex]y=7x-5[/tex]
We can also write it as
[tex]f(x)=7x-5[/tex]
- This means that the function ''f'' depends of the variable x.
- The possible inputs of the function are the values that the "x" can assume.
Now, given a possible ''x'', if we replace it in the expression of f(x) the result will be a possible output that matches that input.
For example, If [tex]x=0[/tex] ⇒
[tex]y=7.(0)-5=-5[/tex]
If x = 0 ⇒ y = -5
The pair [tex](x,y)=(0,-5)[/tex] is a possible input-output pair.
In this exercise we have 4 sets. In order to find a set of possible input-output pairs, we need to replace them in the equation of the function.
- The first set is {(-5,0),(9,2),(-26,-3)}
If we replace each pair in the function :
[tex]0=7(-5)-5=-40[/tex]
[tex]0=-40[/tex]
The pair (-5,0) is not a possible pair of input-output. Therefore,we can't say that all the set is a possible pair of input-output for the function.
- The second set is {(2,7),(1,6),(3,13)}
Replacing each pair in the function :
[tex]7=7.(2)-5=9[/tex]
[tex]7=9[/tex]
Therefore the pair (2,7) is not a possible pair of input-output for the function and we can't say that all the set is a possible input-output set for the function.
- The third set is {(0,-5),(2,9),(-3,-26)}
If we replace each pair in the function
[tex]-5=7.(0)-5[/tex]
[tex]-5=-5[/tex]
The second pair
[tex]9=7.(2)-5=9[/tex]
[tex]9=9[/tex]
The last pair
[tex]-26=7.(-3)-5[/tex]
[tex]-26=-26[/tex]
All pairs match the function. Therefore the third set of pairs is a possible pair of input-output for the function.
- The last set {(1,3),(6,18),(8,15)}
If we replace in the function each pair
[tex]3=7(1)-5=2[/tex]
[tex]3=2[/tex]
The pair (1,3) is not a possible input-output pair for the function. Therefore, we can't say that all the set is a possible input-output set of pairs for the function.
The set {(0,-5),(2,9),(-3,-26)} represents a possible set of input-output pairs for the function.
