The table shows the outputs y for different inputs x: input (x) 5 6 7 8 output (y) 2 5 8 11 part a: do the data in this table represent a function? justify your answer. (3 points) part b: compare the data in the table with the relation f(x) = 2x + 13. which relation has a greater value when x = 7? (2 points) part c: using the relation in part b, what is the value of x if f(x) = 75? (5 points)

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:



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:



Subtract 13 from both sides:



Divide both sides by 2 to get x by itself:



The x value that produces an output of 75 will be 31.