Question

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)

Answer 1

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:


`2(7) + 13 = 14 + 13 = 27`

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:


`2x + 13 = 75`

Subtract 13 from both sides:


`2x = 62`

Divide both sides by 2 to get x by itself:


`\boxed{x = 31}`

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