4. (03.03 HC) The table shows the outputs, y, for different inputs, x:
Input (x) 1 2 3 4
Output (y) 5 5 7 9
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 – 8. Which relation has a greater value when x = 4? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 34? (5 points)
(10 points)

Part A: Yes, the first data represents a function. By the book definition, a function is a relation in which no value of x will have two different values of y. This means that we can have two similar values of y with two different values of x but not the other way around.
None of the numbers for the table of x repeat, therefore we can safely say that the relation is a function.

Part B: For this part, all we have to do is to plug in x = 4 in the 2nd relation,

f(x) = 2(4) – 8 = 0

In the table, when x = 4, y = 9. Therefore the function described in the table has greater value.

Part C: Again all we have to do is to plug in x = 34 in the 2nd relation,
f(x) = 2(34) – 8

f(x) = 60