Question

The table shows the outputs, y, for different inputs, x:

Answer 1

The table shows the outputs, y, for different inputs, x:

Input (x)     1   3   5   7
Output (y)  8   6   5  4

Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Yes, the data in the table represent a function. The reason is that given an input (value of x), in the domain of the function (which is 1, 3, 5, 7), you can state the correspondant output (value of y) without ambiguity.

Part B: Compare the data in the table with the relation f(x) = 4x + 8. Which relation has a greater value when x = 3? (2 points)

x = 3 => f(3) = 4(3) + 8 = 12 + 8 = 20

While the image of 3 in the data is y = 6.

So, the function f(x) = 4x + 8 has a greater value when x = 3.

Part C: Using the relation in Part B, what is the value of x if f(x) = 76? Be sure to show all your work.

f(x) = 76 = 4x + 8 => 4x = 76 - 8 = 68

=> x = 68/4 = 17