Part A:
For a table to be considered a function, every x-value must have one y-value.
Each x-value in this table is unique, and has only one y-value, so this table does represent a function.
Part B:
Plug in 7 for every x in the relation:
[tex]2(7) + 13 = 14 + 13 = 27[/tex]
The table's output when x = 7 is 11. Compare the two outputs:
11 < 27
The relation, 2x + 13, has a greater value when x = 7.
Part C:
Set the relation to equal 75:
[tex]2x + 13 = 75[/tex]
Subtract 13 from both sides:
[tex]2x = 62[/tex]
Divide both sides by 2 to get x by itself:
[tex]\boxed{x = 31}[/tex]
The x value that produces an output of 75 will be 31.
