Question

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

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

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

Part B: Compare the data in the table with the relation f(x) = 4x + 8. Which relation 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?

Answer 1

Hi there!
Let me explain each part to you, along with the answer.
a. Yes, the data represent a function. The definition of a function is a relation in which no value of x will have two different values of y. None of the numbers in the table repeat, so we can safely say that the relation is a function.

b. We are given the function
`f(x)= 4x + 8`. What we are asking to find is which table has a greater output value when x = 3. To start off, we can plug in 3 into the given function.

`f(x) = 4x + 8`

`f(3) = 4(3) + 8`

`f(3) = 12 + 8`

`f(3) = 20`
The output value for the function
`f(x)= 4x + 8` is 20. When we look at the table's output value for 3, we get 6. Therefore,
`f(x)= 4x + 8` has a greater value when x = 3.

c. We are asked to find the output value of the function
`f(x)= 4x + 8` when f(x) is equal to 76. Notice that the problem did not state an x value, but instead a substitution scenario. Hence, we will need to replace f(x) with 76.

`f(x) = 4x + 8`

`76=4x + 8`

`68=4x`

`x = 17`
Therefore, the value of x when f(x) is equal to 76 is 17.

Hope my answer has come of assistance to you and have a magnificent day!

Answer 2

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 correspondent 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