The table shows the outputs y for different inputs x:
input
(x)5678
output
(y)25811
part a: do the data in this table represent a function? justify your answer.
part b: compare the data in the table with the relation f(x) = 2x + 13. which relation has a greater value when x = 7?
part c: using the relation in part b, what is the value of x if f(x) = 75?

Table:

x      y
5      2
6      5
7      8
8      11

Part A: Do the data in this table represent a function? Justify your answer.

Yes, they do. Because for input set is related with a wll defined output, unambiguosly.

Part B: Compare the data in the table with the relation f(x) = 2x + 13. Which relation has a greater value when x = 7?

The relation f(x) = 2x + 13 results in these points

x      f(x)
5      23
6      25
7      27
8      29

The relation f(x) = 2x + 13 has a greater value than the relation of the first table when x =7

Part C: Using the relation in Part B, what is the value of x if f(x) = 75?

f(x) = 2x + 13 = 75 => x = [75 - 13] / 2 = 31

if f(x) = 75, x = 31